3   1822  01342  6820 


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3  1822  01342  6820 


TABLES  OF  ^fl=?  AND  1-r' 

FOR  USE  IN 

PARTIAL  CORRELATION 
AND  IN  TRIGONOMETRY 


BY 
JOHN  RICE  MINER,  Sc.  D. 

Associate  in  the  Department  of  Biometry  and  Vital  Statistics, 

School  of  Hygiene  and  Public  Health,  The 

Johns  Hopkins  University 


THE  JOHNS  HOPKINS  PRESS 

BALTIMORE,  MARYLAND 

1922 


Copyright  1922  by 

The  Johns  Hopkins  Press 

Baltimore,  Md. 


C^e  £ort  ®<xfttmotc  (|)rcee 

BALTIMORE,   MD.,   C.    S.    A. 


TABLES  OF  VT^  AND  1-r-  FOE  USE  IN  PARTIAL  COR- 
RELATION AND  IN  TRIGONOMETRY* 
By  John  Rice  Miner 

ESTTRODUCTION 

In  the  calculation  of  partial  correlation  coefficients  each  coefficient 
is  obtained  from  those  of  the  next  lower  order  by  the  formula : 


I       ^Iw  •  34  •  •  •  (n-1)  ^2n  •  34  •  •  •  (n-l) 


(i) 


'12-34---n—        W-|  _     .  VT^' 

*   ^        '    ln'34-  •  '(n-l)  *   ^        '    2n'34-  •  -(n-l) 

A  large  part  of  the  labor  of  calculation  is  thus  involved  in  the  deter- 
mination of  the  factors  in  tiie  denominator  of  the  formula,  and  may  be 

r^ saved  by  reference  to  a  table  of  Vl— ^  for  different  values  of  r. 

*"  Similarly,  a  standard  deviation  of  higher  order  is  calculated  from  the 

cv  formula: 


<'"l-23-  •  •n~'''i-23-  •  '(n-l)  ^  1       '"lB-23' •  '(n-l)  V^U 

in  which  again  labor  may  be  saved  by  reference  to  such  a  table,  which 
I  have  calculated  at  the  suggestion  of  Dr.  Raymond  Pearl. 

Table  I  gives  the  values  of  Vl  — r^  for  r=:.0001  to  .9999,  for  values 
of  the  argument  proceeding  by  differences  of  .0001.  A  similar  table, 
but  on  a  mudi  less  extended  scale,  has  been  given  by  Holbrook  Working, 
in  Quarterly  Publications  of  the  American  Statistical  Association, 
XVII,  767,  June,  1921.  Since  sin^  a-f  cos^  a=l,  the  table  may  also 
be  used  to  obtain  cos  a  when  sin  a  is  given  and  vice  versa. 

Table  II,  which  gives  the  values  of  1  — r^  on  a  more  extended  scale 
than  Table  VIII  of  Pearson's  Tables  for  Statisticians  and  Biome- 
tricians,  may  be  used  in  the  calcidation  of  the  probable  error  of  the 
correlation  coefficient  from  the  formula: 

PEr=--^  (l-r-^)=Xi(l-r^).  (iii) 

Vn 

'  Papers  from  the  Department  of  Biometry  and  Vital  Statistics,  School  of 
Hygiene  and  Public  Health,  Johns  Hopkins  University,  No.  55. 

(8) 


In  calculating  the  tables  the  value  of  1  — r^  was  obtained  for  each 
value  of  r  and  its  square  root  then  calculated  by  dividing  1  —  r '  by  an 
approximate  value  of  the  square  root  and  taking  the  mean  of  the 
divisor  and  quotient.    This  method  of  obtaining  square  roots  depends 

x^  S- 

on  the  fact  that r  =x  —  h-\ If,  therefore,  8  is  small  as 

x+o  X 

compared  with  x  the  quotient  will  be  nearly  equal  to  x  — 8  and  the 
mean  of  divisor  and  quotient  will  be  a  much  closer  approximation  to 
x  than  the  original  a; +  8.  Where,  as  in  the  greater  part  of  this  table,  a 
close  approximation  to  the  square  root  can  be  found  by  differences 
from  the  preceding  items,  this  method  is  very  convenient.  All  work 
was  done  on  a  calculating  machine  and  each  table  checked  by 
differences. 

In  arrangement  the  tables  are  in  general  like  logarithmic  tables. 
The  column  at  the  left  of  the  page  gives  the  first  three  figures  of  r, 
while  the  fourth  figure  is  given  in  the  heading.  To  find  the  value  of 
Vl— r^  for  a  given  value  of  r,  we  therefore  look  in  Table  I  for  the  first 
three  figures  of  r  (including  zeros)  in  the  coltmm  at  the  left  of  the 
page  headed  r.  In  the  same  line  and  in  the  column  headed  by  the 
fourth  figure  of  r  we  find  the  last  figures  of  V^l  — r^.  For  r=:.0000 
to  .7000  the  first  three  figures  of  Vl  — r^  are  given  as  the  separated 
figures  in  tiie  column  headed  0.  Should  there  be  no  separated  figures 
in  column  0  in  this  line  the  three  standing  next  above  should  be  taken, 
except  when  the  first  of  the  figures  in  the  column  headed  by  the  fourth 
figure  of  r  has  a  bar  above  it,  when  we  must  take  the  separated  figures 
from  the  Hne  below  in  column  0.  For  r=.7000  to  .8500  the  first  three 
figures  of  Vl— r^  are  given  in  column  0  and  column  5.  If,  therefore, 
the  fourth  figure  of  r  is  between  0  and  4,  inclusive,  the  first  three 
figures  of  yfl  —  r^  are  to  be  taken  from  column  0  in  the  same  line, 
except  when  there  is  a  bar  over  the  first  figure  in  the  column  headed 
by  the  fourth  figure  of  r,  in  which  case  the  first  three  figures  of  Vl  — r^ 
are  found  in  coliunn  5  in  the  same  line.  If  the  fourth  figure  of  r  is 
between  5  and  9,  inclusive,  the  first  three  figures  of  Vl  — r^  are  to  be 
taken  from  column  5  in  the  same  line,  except  when  there  is  a  bar  over 
the  first  figure  in  the  column  headed  by  the  fourth  figure  of  r,  in  which 
case  the  first  three  figures  of  Vl  — t^  are  to  be  taken  from  column  0  of 
the  line  below.  For  r=.8500  to  .9999  aU  the  figures  of  Vl-r^  are 
given  in  each  column. 

(4) 


For  example,  if  r=.0476  we  find  the  first  three  fibres  .047  in  the 
column  T  on  page  7.  In  the  same  line  and  in  the  column  6  we  find 
the  figures  866.  The  separated  figures  in  the  column  0  next  above 
the  line  are  .998,  and  Vl-f^  is  therefore  .998  866.  If  r  =  .1944  we 
find  .194  in  the  column  r  on  page  10.  In  the  same  line  and  in  the 
column  4  we  find  the  figures  922.  Since  there  is  a  bar  over  the  first 
figure  we  take  the  .980  from  the  line  below  in  column  0,  and  Vl  — r^ 
is  .980  922.  If  r  =.7432  we  find  .743  in  the  column  r  on  page  21.  In 
the  same  line  in  column  2  we  find  069  and  in  column  0  the  first  three 
figures  .669,  so  that  y/Y^r"  is  .699  069.  If  r=.7433  we  find  in 
column  3  of  the  same  line  958.  Since  there  is  a  bar  over  the  first 
figure,  we  take  the  .668  from  column  5,  and  y/l  —  r^  is  .668  958.  If 
r=.7757  we  find  .775  in  column  r  on  page  22.  In  column  7  of  the 
same  line  we  find  102  and  in  column  5  the  first  three  figures  .631,  so 
that  Vl-r^  is  .631  102.  If  r=.7758  in  column  8  of  the  same  line 
we  find  979.  As  there  is  a  bar  over  the  first  figure  we  take  .630  from 
column  0  of  the  line  below,  and  Vl-r^  is  .630  979.  If  r=.8937  we 
find  .893  in  column  r  on  page  25  and  in  column  7  of  the  same  line  find 
Vl— ^  to  be  .448  665.  If  r  is  given  to  more  than  four  places  of 
decimals  the  value  of  Vl  — r^  may  if  desired  be  obtained  by  the  usual 
methods  of  interpolation. 

Probably  the  most  advantageous  form  in  which  to  arrange  the  cal- 
culation of  partial  correlation  coefficients  is  the  following : 


Coefficient 

Vl— r2 

Product  term 

Numerator 

Denominator 

Coeffi 

cient 

^12 

+  .0476 

.998  87 

+  .144  48 

—  .096  88 

.656  30 

r-i-.s 

—  .1476 

ri3 

+  .1944 

.980  92 

+  .035  38 

+  .159  02 

.668  31 

n3-2 

+  .2379 

r^ 

+ . 7432 

. 669  07 

+  .009  25 

+  .733  95 

.979  SI 

»"23- 

+  .7491 

The  derivation  of  the  Vl— r^  column  from  Table  I  has  already 
been  explained.  In  the  product  term  column  +.144  48  is  the  product 
of  +.1944  and  +.7432,  while  the  other  items  are  similarly  derived. 
In  the  numerator  column  -.096  88=  (  +  .0476)  -  (  +  .144  48),  while 
.65630  in  the  denominator  column  is  the  product  of  .980  92  and 
.669  07  from  the  Vl-r^  column.  In  the  last  column  -.1476  is  the 
quotient  of  -.096  88  divided  by  .656  30. 

(5) 


The  arrangement  of  Table  II  is  similar  to  that  of  Table  I,  except 
that  for  r=:.0000  to  .5000  the  first  three  figures  of  1  — r^  are  given  in 
column  0,  while  for  r=.5000  to  .9999  they  are  given  in  both  column  0 
and  column  5.  To  obtain  the  probable  error  of  r,  1  — r^  from  Table  II 
is  multiplied  by  xi  from  Table  V  of  Pearson's  Tables  for  Statisticians 
and  Biometricians.  For  example,  if  for  a  population  of  453, 
r=— .5627,  we  find  .562  in  column  r  of  Table  II  on  page  41,  In 
column  7  of  the  same  line  we  find  369.  As  r  is  between  .5000  and 
.9999  we  look  in  column  5  for  the  first  three  figures  .683,  so  that 
l-r"  is  .683  369.  From  Table  V  we  find  xi  =  . 03169  for  n  =  453. 
Therefore,  the  probable  error  of  r=. 03169 X. 683  369  =  .0217. 


(e> 


Table  I.     Values  of  Vl=? 

r  0  1234S6789 

.000       1.000  000  000  000  000  000  000  000  000  000  000 

.001          .999  999  999  999  999  999  999  999  999  998  998 

.002  998  998  998  997  997  997  997  996  996  996 

.003  995  995  995  995  994  994  994  993  993  992 

,004  992  992  991  991  990  990  989  989  988  988 

.OOS  987  987  986  986  985  985  984  984  983  983 

.006  982  981  981  980  980  979  978  978  977  976 

.007  975  975  974  973  973  972  971  970  970  969 

.908  968  967  966  966  965  964  963  962  961  960 

.009  959  959  958  957  956  955  954  953  952  951 

.010  950  949  948  947  946  945  944  943  942  941 

.011  939  938  937  936  935  934  933  932  930  929 

.012  928  927  926  924  923  922  921  919  918  917 

.013  915  914  913  912  910  909  908  906  905  903 

.014  902  901  899  898  896  895  893  892  890  889 

.OlS  888  886  884  883  881  880  878  877  875  874 

.016  872  870  869  867  866  864  862  861  859  857 

.017  855  854  852  850  849  847  845  843  842  840 

.018  838  836  834  833  831  829  827  825  823  821 

.019  819  818  816  814  812  810  808  806  804  802 

.020  800  798  796  794  792  790  788  786  784  782 

.021  779  777  775  773  771  769  767  765  762  760 

.022  758  756  754  751  749  747  745  742  740  738 

.023  735  733  731  729  726  724  721  719  717  714 

.024  712  710  707  705  702  700  697  695  692  690 

.02S  687  685  682  680  677  675  672  670  667  665 

.026  662  659  657  654  651  649  646  643  641  638 

.027  635  633  630  627  625  622  619  616  614  611 

.028  608  605  602  599  597  594  591  588  585  582 

.029  579  577  574  571  568  565  562  559  556  553 

.030  550  547  544  541  538  535  532  529  526  522 

.031  519  516  513  51t)  507  504  501  497  494  491 

.032  488  485  481  478  475  472  468  465  462  459 

.033  455  452  449  445  442  439  435  432  429  425 

.034  422  418  415  412  408  405  401  398  394  391 

.033  387  384  380  377  373  370  366  363  359  355 

.036  352  348  345  341  337  334  330  326  323  319 

.037  315  312  308  304  300  297  293  289  285  282 

.038  278  274  270  266  262  259  255  251  247  243 

.039  239  235  231  227  224  220  216  212  208  204 

.040  200  196  192  188  184  180  175  171  167  163 

.041  159  155  151  147  143  139  134  130  126  122 

.042  118  113  109  105  101  096  092  088  084  079 

.043  075  071  066  062  058  053  049  045  040  036 

.044  032  027  023  018  014  009  005  000  996  991 

.045         .998  987  982  978  973  969  964  960  955  951  946 

.046  941  937  932  928  923  918  914  909  904  900 

.047  895  890  885  881  876  871  866  862  857  852 

.048  847  843  838  833  828  823  818  813  809  804 

.049  799  794  789  784  779  774  769  764  759  754 

.OSO  749  744  739  734  729  724  719  714  709  704 

(7) 


Table  I.    Values  of  VT^? 


r  0  123456789 

.050          .998  749  744  739  734  729  724  719  714  709  704 

.051  699  694  688  683  678  673  668  663  657  652 

.052  647  642  637  631  626  621  616  610  605  600 

.053  595  589  584  579  573  568  562  557  552  546 

.054  541  536  530  525  519  514  508  503  497  492 

.055  486  481  475  470  464  459  453  448  442  436 

.056  431  425  420  414  408  403  397  391  386  380 

.057  374  368  363  357  351  346  340  334  328  322 

.058  317  311  305  299  293  287  282  276  270  264 

.059  258  252  246  240  234  228  222  216  210  204 

.060  198  192  186  180  174  168  162  156  150  144 

.061  138  132  126  119  113  107  101  095  089  082 

.062  076  070  064  057  051  045  039  032  026  020 

.063  014  007  001  995  988  982  976  969  963  956 

.064          .997  950  943  937  931  924  918  911  905  898  892 

.065  885  879  872  866  859  853  846  839  833  826 

.066  820  813  806  800  793  786  780  773  766  760 

.067  753  746  740  733  726  719  713  706  699  692 

068  685  679  672  665  658  651  644  637  631  624 

.069  617  610  603  596  589  582  575  568  561  554 

.070  547  540  533  526  519  512  505  498  491  483 

071  476  469  462  455  448  441  433  426  419  412 

072  405  397  390  383  376  368  361  354  347  339 
.073  332  325  317  310  303  295  288  280  273  266 

074  258  251  243  236  228  221  214  206  199  191 

.075  184  176  168  161  153  146  138  131  123  115 

.076  108  100  093  085  077  070  062  054  047  039 

,077  031  023  016  008  000  992  985  977  969  961 

.078          .996  953  946  938  930  922  914  906  898  891  883 

.079  875  867  859  851  843  835  827  819  811  803 

.080  795  787  779  771  763  755  747  738  730  722 

.081  714  706  698  690  682  673  665  657  649  641 

082  632  624  616  608  599  591  583  574  566  558 

083  550  541  533  525  516  508  499  491  483  474 
.084  466  457  449  440  432  423  415  406  398  389 
.085  381  372  364  355  347  338  330  321  312  304 

.086  295  286  278  269  261  252  243  234  226  217 

.087  208  200  191  182  173  165  156  147  138  129 

.088  120  112  103  094  085  076  067  058  049  041 

.089  032  023  014  005  996  987  978  969  960  951 

.090          .995  942  933  924  915  906  896  887  878  869  860 

.091  851  842  833  823  814  805  796  787  778  768 

.092  759  750  741  731  722  713  703  694  685  675 

.093  666  657  647  638  629  619  610  600  591  582 

094  572  563  553  544  534  525  515  506  496  487 

.095  477  468  458  449  439  429  420  410  401  391 

.096  381  372  362  352  343  333  323  314  304  294 

.097  284  275  265  255  245  236  226  216  206  196 

.098  186  177  167  157  147  137  127  117  107  097 

.099  087  077  068  058  048  038  028  018  008  997 

.100          .994  987  977  967  957  947  937  927  917  907  897 

(8) 


Table  I.    Values  of  ^/U^^ 

r  0  123456789 

.too  .994  987  977  967  957  947  937  927  917  907  897 

.101  886  876  866  856  846  836  825  815  805  795 

.102  784  774  764  754  743  733  723  712  702  692 

.103  681  671  661  650  640  629  619  609  598  588 

.104  577  567  556  546  535  525  514  504  493  483 

.105  472  462  451  441  430  419  409  398  387  377 

.106  366  355  345  334  323  313  302  291  281  270 

.107  259  248  237  227  216  205  194  183  173  162 

.108  151  140  129  118  107  096  086  075  064  053 

.109  042  031  020  009  998  987  976  965  954  943 

.110  .993  932  921  909  898  887  876  865  854  843  832 

.111  820  809  798  787  776  764  753  742  731  719 

.112  708  697  686  674  663  652  640  629  618  606 

.113  595  584  572  561  549  538  527  515  504  492 

.114  481  469  458  446  435  423  412  400  389  377 

.lis  365  354  342  331  319  307  296  284  273  261 

.116  249  238  226  214  202  191  179  167  155  144 

.117  132  120  1_08  097  085  073  061  049  037  025 

.118  014  002  990  978  966  954  942  930  918  906 

.119  .992  894  882  870  858  846  834  822  810  798  786 

.120  774  762  750  738  725  713  701  689  677  665 

.121  653  640  628  616  604  591  579  567  555  542 

.122  530  518  505  493  481  469  456  444  431  419 

.123  407  394  382  369  357  345  332  320  307  295 

.124  282  270  257  245  232  220  207  194  182  169 

.123  157  144  132  119  106  094  081  068  056  043 

.126  030  018  005  992  979  967  954  941  928  916 

.127  .991  903  890  877  864  851  839  826  813  800  787 

.128  774  761  748  735  722  710  697  684  671  658 

.129  645  632  619  606  592  579  566  553  540  527 

.130  514  501  488  475  461  448  435  422  409  396 

.131  382  369  356  343  329  316  303  290  276  263 

,132  250  236  223  210  196  183  170  156  143  129 

.133  116  103  089  076  062  049  035  022  008  995 

.134  .990  981  968  954  941  927  914  900  886  873  859 

.135  846  832  818  805  791  777  764  750  736  723 

.136  709  695  681  668  654  640  626  612  599  585 

.137  571  557  543  530  516  502  488  474  460  446 

.138  432  418  404  390  376  362  348  334  320  306 

.139  292  278  264  250  236  222  208  194  180  166 

.140  152  137  123  109  095  081  066  052  038  024 

.141  010  995  981  967  953  938  924  910  895  881 

.142  .989  867  852  838  824  809  795  780  766  752  737 

.143  723  708  694  679  665  650  636  621  607  592 

.144  578  563  549  534  519  505  490  476  461  446 

.145  432  417  402  388  373  358  344  329  314  299 

.146  285  270  255  240  225  211  196  181  166  151 

147  136  122  107  092  077  062  047  032  017  002 

148  .988  987  972  957  942  927  912  897  882  867  852 
.149  837  822  807  792  777  762  747  731  716  701 

ISO  686  671  656  640  625  610  595  580  564  549 

(9) 


Table  I.     Values  of  \/l=7 

r  0               1234S6789 

.ISO  .988  686  671  656  640  625  610  595  580  564  549 

.ISt  534  518  503  488  473  457  442  427  411  396 

.132  380  365  350  334  319  303  288  273  257  242 

.153  226  211  195  180  164  1_49  1^33  118  1_02  086 

.154  071  055  040  024  008  993  977  961  946  930 

.155  .987  914  899  883  867  852  836  820  804  789  773 

.156  757  741  725  710  694  678  662  646  630  614 

.157  599  583  567  551  535  519  503  487  471  455 

.15S  439  423  407  391  375  359  343  327  311  295 

.159  279  262  246  230  214  198  182  166  M9  1,33 

.160  117  101  085  068  052  036  020  003  987  971 

.161  .986  954  938  922  905  889  873  856  840  824  807 

.162  791  774  758  741  725  709  692  676  659  643 

.163  626  610  593  576  560  543  527.  510  494  477 

.164  460  444  427  410  394  377  360  344  327  310 

.165  294  277  260  243  227  210  193  176  159  143 

.166  126  109  092  075  058  041  025  008  991  974 

.167  .985  957  940  923  906  889  872  855  838  821  804 

.168  787  770  753  736  719  702  685  667  650  633 

.169  616  599  582  565  547  530  513  496  479  461 

.170  444  427  410  392  375  358  340  323  306  288 

.171  271  254  236  219  202  184  1_67  149  132  114 

.172  097  079  062  045  027  010  992  974  957  939 

.173  .984  922  904  887  869  851  834  816  799  781  763 

.174  746  728  710  693  675  657  639  622  604  586 

.175  568  551  533  515  497  479  462  444  426  408 

.176  390  372  354  336  319  301  283  265  247  229 

.177  211  193  1,75  157  139  121  103  085  067  049 

.178  030  012  994  976  958  940  922  904  885  867 

.179  .983  849  831  813  794  776  758  740  721  703  685 

.180  667  648  630  612  593  575  557  538  520  501 

.181  483  465  446  428  409  391  372  354  336  317 

.182  299  280  261  243  224  206  187  169  150  132 

.183  113  094  076  057  038  020  001  982  964  945 

.184  .982  926  908  889  870  852  833  814  795  776  757 

.185  739  720  701  682  663  644  625  606  588  569 

.186  550  531  512  493  474  455  436  417  398  379 

.187  360  341  322  303  284  265  246  226  207  188 

.188  169  150  131  112  092  073  054  035  016  996 

.189  .981977  958  939  919  900  881  861  842  823  803 

.190  784  765  745  726  707  687  668  648  629  609 

.191  590  571  551  532  512  493  473  454  434  414 

.192  395  375  356  336  317  297  277  258  238  218 

.193  199  179  159  MO  120  100  081  061  041  021 

.194  002  982  962  942  922  903  883  863  843  823 

.195  .980  803  783  763  744  724  704  684  664  644  624 

.196  604  584  564  544  524  504  484  464  444  424 

,197  403  383  363  343  323  303  283  263  242  222 

,198  202  182  162  141  121  101  081  060  040  020 

.199  .979  999  979  959  939  918  898  877  857  837  816 

,200  796  775  755  735  714  694  673  653  632  612 

(10) 


Table  I.  Values  of  V^ 

-r* 

r 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

200 

.979  796 

775 

755 

735 

714 

694 

673 

653 

632 

612 

201 

591 

571 

550 

530 

509 

489 

468 

447 

427 

406 

202 

386 

365 

344 

324 

303 

282 

262 

241 

220 

199 

203 

179 

158 

137 

116 

096 

075 

054 

033 

013 

992 

204 

.978  971 

950 

929 

908 

887 

867 

846 

825 

804 

783 

205 

762 

741 

720 

699 

678 

657 

636 

615 

594 

573 

206 

552 

531 

510 

489 

468 

447 

425 

404 

383 

362 

207 

341 

320 

299 

277 

256 

235 

214 

193 

171 

150 

208 

129 

108 

086 

065 

044 

022 

001 

980 

958 

937 

209 

.977  916 

894 

873 

851 

830 

809 

787 

766 

744 

723 

210 

701 

680 

658 

637 

615 

594 

572 

551 

529 

508 

211 

486 

464 

443 

421 

400 

378 

356 

335 

313 

291 

212 

270 

248 

226 

205 

183 

161 

139 

118 

096 

074 

213 

052 

030 

009 

987 

965 

943 

921 

899 

877 

856 

214 

.976  834 

812 

790 

768 

746 

724 

702 

680 

658 

636 

215 

614 

592 

570 

548 

526 

504 

482 

460 

438 

415 

216 

393 

371 

349 

327 

305 

283 

260 

238 

216 

194 

217 

172 

149 

127 

105 

083 

060 

038 

016 

993 

971 

218 

.975  949 

926 

904 

882 

859 

837 

815 

792 

770 

747 

219 

725 

703 

680 

657 

635 

612 

590 

567 

545 

522 

220 

500 

477 

455 

432 

410 

387 

364 

342 

319 

296 

221 

274 

251 

228 

206 

183 

160 

138 

115 

092 

069 

222 

047 

024 

001 

978 

956 

933 

910 

887 

864 

841 

223 

.974  818 

796 

773 

750 

727 

704 

681 

658 

635 

612 

224 

589 

566 

543 

520 

497 

474 

451 

428 

405 

382 

225 

359 

336 

313 

289 

266 

243 

22b 

197 

174 

150 

226 

127 

104 

081 

058 

034 

Oil 

988 

965 

941 

918 

227 

.973  895 

871 

848 

825 

801 

778 

755 

731 

708 

685 

228 

661 

638 

614 

591 

567 

544 

520 

497 

473 

450 

229 

426 

403 

379 

356 

332 

309 

285 

261 

238 

214 

230 

191 

167 

143 

120 

096 

072 

049 

025 

001 

977 

231 

.972  954 

930 

906 

882 

859 

835 

811 

787 

763 

740 

232 

716 

692 

668 

644 

620 

596 

572 

549 

525 

501 

233 

477 

453 

429 

405 

381 

357 

333 

309 

285 

261 

234 

237 

213 

188 

164 

140 

116 

092 

068 

044 

020 

.235 

.971  995 

971 

947 

923 

899 

874 

850 

826 

802 

777 

.236 

753 

729 

704 

680 

656 

631 

607 

583 

558 

534 

.237 

510 

485 

461 

436 

412 

388 

363 

339 

314 

290 

.238 

265 

241 

216 

192 

167 

142 

118 

093 

069 

044 

.239 

020 

995 

970 

946 

921 

896 

872 

847 

822 

798 

.240 

.970  773 

748 

723 

699 

674 

649 

624 

600 

575 

550 

.241 

525 

500 

475 

451 

426 

401 

376 

351 

326 

301 

.242 

276 

251 

226 

201 

176 

151 

126 

101 

076 

051 

.243 

026 

001 

976 

951 

926 

901 

876 

851 

826 

800 

.244 

.969  775 

750 

725 

700 

675 

649 

624 

599 

574 

548 

.245 

523 

498 

473 

447 

422 

397 

371 

346 

321 

295 

.246 

270 

244 

219 

194 

168 

143 

117 

092 

066 

041 

.247 

015 

990 

964 

939 

913 

888 

862 

837 

811 

786 

.248 

.968  760 

734 

709 

683 

658 

632 

606 

581 

555 

529 

.249 

503 

478 

452 

426 

401 

375 

349 

323 

297 

272 

.250 

246 

220 

194 

168 

142 

117 

091 

065 

039 

013 

(11) 


Table  I.     Values  of  Vl=? 

r  0  123456789 

.250  .968  246  220  194  168  142  117  091  065  039  013 

.251  .967  987  961  935  909  883  857  831  805  779  753 

.252  727  701  675  649  623  597  571  545  519  492 

.253  466  440  414  388  362  335  309  283  257  230 

.254  204  178  152  125  099  073  046  020  994  967 

.255  .966  941  915  888  862  835  809  783  756  730  703 

.256  677  650  624  597  571  544  518  491  465  438 

.257  411  385  358  332  305  278  252  225  198  172 

.258  145  118  091  065  038  Oil  984  958  931  904 

.259  .965  877  851  824  797  770  743  716  689  662  636 

.260  609  582  555  528  501  474  447  420  393  366 

.261  339  312  285  258  231  203  176  149  122  095 

.262  068  041  014  986  959  932  905  878  850  823 

.263  .964  796  769  741  714  687  659  632  605  577  550 

.264  523  495  468  441  413  386  358  331  303  276 

.265  248  221  193  166  138  111  083  056  028  001 

.266  .963  973  945  918  890  863  835  807  780  752  724 

.267  697  669  641  613  586  558  530  502  475  447 

.268  419  391  363  335  308  280  252  224  1,96  168 

.269  140  112  084  056  028  000  972  944  916  888 

.270  .962  860  832  804  776  748  720  692  664  636  607 

.271  579  551  523  495  467  438  410  382  354  326 

.272  297  269  241  212  184  156  127  099  071  042 

.273  014  986  957  929  900  872  844  815  787  758 

.274  .961  730  701  673  644  616  587  559  530  501  473 

.275  AAA  416  387  358  330  301  272  244  215  186 

.276  158  129  100  071  043  014  985  956  928  899 

.277  .960  870  841  812  783  755  726  697  668  639  610 

.278  581  552  523  494  465  436  407  378  349  320 

.279  291  262  233  204  175  146  117  087  058  029 

.280  000  971  942  912  883  854  825  796  766  737 

.281  .959  708  678  649  620  591  561  532  503  473  444 

.282  414  385  356  326  297  267  238  208  179  149 

.283  120  090  061  031  002  972  943  913  883  854 

.284  .958  824  795  765  735  706  676  646  617  587  557 

.285  528  498  468  438  408  379  349  319  289  259 

.286  230  200  170  140  110  080  050  020  990  961 

.287  .957  931  901  871  841  811  781  751  721  691  660 

.288  630  600  570  540  510  480  450  420  389  359 

.289  329  299  269  238  208  178  148  118  087  057 

.290  027  996  966  936  905  875  845  814  784  753 

.291  .956  723  693  662  632  601  571  540  510  479  449 

.292  418  388  357  327  296  266  235  204  174  \AZ 

.293  112  082  051  020  990  959  928  898  867  836 

.294  .955  805  775  744  713  682  651  621  590  559  528 

.295  497  466  435  405  374  343  312  281  250  219 

.296  188  157  126  095  064  033  002  971  940  909 

.297  .954  877  846  815  784  753  722  691  659  628  597 

.298  566  535  503  472  441  410  378  347  316  284 

.299  253  222  190  159  128  096  065  033  002  971 

.300  .953  939  908  876  845  813  782  750  719  687  656 

(12) 


Table  L    Values  of  VT^? 

r  0  123456789 

.300  .953  939  908  876  845  813  782  750  719  687  656 

.301  624  593  561  529  498  466  435  403  371  340 

.302  308  276  245  213  181  149  118  086  054  022 

.303  .952  991  959  927  895  863  831  800  768  736  704 

.304  672  640  608  576  544  512  480  448  416  384 

.305  352  320  288  256  224  192  160  128  096  064 

.306  032  999  967  935  903  871  838  806  774  742 

.307  ,951  710  677  645  613  580  548  516  483  451  419 

.308  386  354  322  289  257  224  192  159  127  095 

.309  062  030  997  965  932  899  867  834  802  769 

.310  .950  737  704  671  639  606  573  541  508  475  443 

.311  410  377  344  312  279  246  213  181  148  115 

.312  082  049  016  984  951  918  885  852  819  786 

.313  .949  753  720  687  654  621  588  555  522  489  456 

.314  423  390  357  324  291  257  224  191  158  125 

.315  092  058  025  992  959  926  892  859  826  792 

.316  .948  759  726  693  659  626  593  559  526  492  459 

.317  426  392  359  325  292  258  225  191  158  124 

.318  091  057  024  990  956  923  889  856  822  788 

.319  .947  755  721  687  654  620  586  553  519  485  451 

.320  418  384  350  316  282  249  215  181  147  113 

.321  079  045  Oil  977  944  910  876  842  808  774 

.J22  .946  740  706  672  638  604  569  535  501  467  433 

.323  399  365  331  297  262  228  194  160  126  091 

.324  057  023  989  954  920  886  851  817  783  748 

.325  .945  714  680  645  611  576  542  508  473  439  404 

.326  370  335  301  266  232  197  163  128  094  059 

.327  024  990  955  920  886  851  817  782  747  712 

.328  .944  678  643  608  574  539  504  469  434  400  365 

.329  330  295  260  225  190  156  121  086  051  016 

.330  .943  981  946  911  876  841  806  771  736  701  666 

.331  631  596  561  525  490  455  420  385  350  315 

.332  279  244  209  174  139  103  068  033  997  962 

.333  .942  927  892  856  821  785  750  715  679  644  609 

.334  573  538  502  467  431  396  360  325  289  254 

.335  218  183  147  111  076  040  005  969  933  898 

.336  .941  862  826  791  755  719  683  648  612  576  540 

.337  505  469  433  397  361  326  290  254  218  182 

.338  146  110  074  038  002  966  930  894  858  822 

.339  .940  786  750  714  678  642  606  570  534  498  462 

.340  425  389  353  317  281  245  208  172  136  100 

.341  063  027  991  954  918  882  845  809  773  736 

.342  .939  700  664  627  591  554  518  481  445  408  372 

.343  335  299  262  226  189  153  116  080  043  006 

.344  .938  970  933  896  860  823  786  750  713  676  639 

.345  603  566  529  492  456  419  382  345  308  271 

.346  235  198  161  124  087  050  013  976  939  902 

.347  .937  865  828  791  754  717  680  643  606  569  532 

.348  495  457  420  383  346  309  272  234  197  160 

.349  123  085  048  Oil  974  936  899  862  824  787 

.350  .936  750  712  675  638  600  563  525  488  450  413 

(13) 


Table  I.     Values  of  >/!=? 

r  0  123456789 

.350  .936  750  712  675  638  600  563  525  488  450  413 

.351  375  338  300  263  225  188  150  1.13  075  038 

.352  000  962  925  887  849  812  774  736  699  661 

.353  .935  623  586  548  510  472  435  397  359  321  283 

.354  245  208  170  132  094  056  018  980  942  904 

.355  .934  866  828  790  752  714  676  638  600  562  524 

.356  486  448  410  372  333  295  257  219  181  143 

.357  104  066  028  990  951  913  875  837  798  760 

.358  .933  722  683  645  607  568  530  491  453  414  376 

.359  338  299  261  222  184  145  107  068  029  991 

.360  .932  952  914  875  836  798  759  721  682  643  605 

.361  566  527  488  450  411  372  333  295  256  217 

.362  178  139  100  062  023  984  945  906  867  828 

.363  .931  789  750  711  672  633  594  555  516  477  438 

.364  399  360  321  282  243  203  164  125  086  047 

.365  008  968  929  890  851  811  772  733  693  654 

.366  .930  615  576  536  497  457  418  379  339  300  260 

.367  221  181  142  103  063  024  984  944  905  865 

.368  .929  826  786  747  707  667  628  588  548  509  469 

.369  429  390  350  310  270  231  191  151  ni  072 

.370  032  992  952  912  872  832  793  753  713  673 

.371  .928  633  593  553  513  473  433  393  353  313  273 

.372  233  193  153  112  072  032  992  952  912  872 

.373  .927  831  791  751  711  670  630  590  550  509  469 

.374  429  388  348  308  267  227  187  146  106  065 

.375  025  984  944  903  863  822  782  741  701  660 

.376  .926  620  579  538  498  457  417  376  335  295  254 

.377  213  173  132  091  050  010  969  928  887  846 

.378  .925  806  765  724  683  642  601  560  519  479  438 

.379  397  356  315  274  233  192  151  110  069  028 

.380  .924  986  945  904  863  822  781  740  699  657  616 

.381  575  534  493  451  410  369  328  286  245  204 

.382  162  121  080  038  997  955  914  873  831  790 

.383  .923  748  707  665  624  582  541  499  458  416  375 

.384  333  291  250  208  167  125  083  042  000  958 

.385  .922  917  875  833  791  750  708  666  624  582  541 

.386  499  457  415  373  331  289  247  206  164  122 

.387  080  038  996  954  912  870  828  786  744  701 

.388  .921  659  617  -575  533  491  449  407  364  322  280 

.389  238  196  153  111  069  026  984  942  900  857 

.390  .920  815  772  730  688  645  603  561  518  476  433 

.391  391  348  306  263  221  178  136  093  050  008 

.392  .919  965  923  880  837  795  752  709  667  624  581 

.393  538  496  453  410  367  325  282  239  196  153 

.394  110  068  025  982  939  896  853  810  767  724 

.395  .918  681  638  595  552  509  466  423  380  337  294 

.396  251  207  164  121  078  035  992  948  905  862 

.397  .917  819  775  732  689  645  602  559  516  472  429 

.398  385  342  299  255  212  168  125  081  038  994 

.399  .916  951  907  864  820  777  733  690  646  602  559 

.400  515  471  428  384  340  297  253  209  166  122 

(14) 


Table  I.    Values  of  ^/U^ 

r  0  123456789 

.400  .916  515  471  428  384  340  297  253  209  166  122 

.401  078  034  990  947  903  859  815  771  727  684 

.402  .915  640  596  552  508  464  420  376  332  288  244 

.403  200  156  112  068  024  980  936  891  847  803 

.404  .914  759  715  671  626  582  538  494  450  405  361 

.405  317  272  228  184  139  095  051  006  962  917 

.406  .913  873  829  784  740  695  651  606  562  517  473 

.407  428  384  339  294  250  205  161  116  071  027 

.408  .912  982  937  893  848  803  758  714  669  624  579 

.409  534  490  445  400  355  310  265  220  175  130 

.410  086  041  996  951  906  861  816  771  725  680 

.411  .911  635  590  545  500  455  410  365  319  274  229 

.412  184  139  093  048  003  958  912  867  822  776 

.413  .910  731  686  640  595  550  504  459  413  368  322 

.414  277  231  186  140  095  049  004  958  913  867 

.415  .909  821  776  730  685  639  593  547  502  456  410 

.416  365  319  273  227  182  136  090  044  998  952 

.417  .908  906  861  815  769  723  677  631  585  539  493 

.418  447  401  355  309  263  217  171  125  078  032 

.419  .907  986  940  894  848  802  755  709  663  617  570 

.420  524  478  432  385  339  293  246  200  153  107 

.421  061  014  968  921  875  828  782  735  689  642 

.422  .906  596  549  503  456  410  363  316  270  223  176 

.423  130  083  036  990  943  896  849  803  756  709 

.424  .905  662  615  569  522  475  428  381  334  287  240 

.425  193  146  099  052  005  958  911  864  817  770 

.426  .904  723  676  629  582  535  488  440  393  346  299 

.427  252  204  157  110  063  015  968  921  873  826 

.428  .903  779  731  684  637  589  542  494  447  399  352 

.429  304  257  209  162  114  067  019  972  924  877 

.430  .902  829  781  734  686  638  591  543  495  447  400 

.431  352  304  256  209  161  113  065  017  969  921 

.432  .901  874  826  778  730  682  634  586  538  490  442 

.433  394  346  298  250  202  154  105  057  009  961 

.434  .900  913  865  816  768  720  672  624  575  527  479 

.435  430  382  334  285  237  189  140  092  044  995 

.436  .899  947  898  850  801  753  704  656  607  559  510 

.437  462  413  364  316  267  218  170  121  072  024 

.438  .898  975  926  877  829  780  731  682  634  585  536 

.439  487  438  389  340  292  243  194  145  096  047 

.440  .897  998  949  900  851  802  753  704  654  605  556 

.441  507  458  409  360  310  261  212  163  114  064 

.442  015  966  916  867  818  769  719  670  620  571 

.443  .896  522  472  423  373  324  274  225  175  126  076 

.444  027  977  928  878  828  779  729  680  630  580 

.445  .895  531  481  431  381  332  282  232  182  133  083 

.446  033  983  933  883  834  784  734  684  634  584 

.447  .894  534  484  434  384  334  284  234  184  134  084 

.448  034  983  933  883  833  783  733  682  632  582 

.449  .893  532  481  431  381  331  280  230  180  129  079 

.450  029  978  928  877  827  776  726  675  625  574 

(15) 


Table  I.     Vadues  of  VI — r^ 


r  0  123456789 

.450  .893  029  978  928  877  827  776  726  675  625  574 

.451  .892  524  473  423  372  322  271  221  170  119  069 

.452  018  967  917  866  815  764  714  663  612  561 

.453  .891511  460  409  358  307  256  205  154  104  053 

.454  002  951  900  849  798  747  696  645  594  543 

.455  .890  491  440  389  338  287  236  185  133  082  031 

.456  .889  980  929  877  826  775  723  672  621  569  518 

.457  467  415  364  312  261  210  158  107  055  004 

.458  .888  952  901  849  798  746  694  643  591  540  488 

.459  436  385  333  281  229  178  126  074  022  971 

.460  .887  919  867  815  763  712  660  608  556  504  452 

.461  400  348  296  244  192  140  088  036  984  932 

.462  .886  880  828  776  724  671  619  567  515  463  411 

.463  358  306  254  202  149  097  045  992  940  888 

.464  .885  835  783  730  678  626  573  521  468  416  363 

.465  311  258  206  153  100  048  995  943  890  837 

.466  .884  785  732  679  627  574  521  468  416  363  310 

.467  257  204  152  099  046  993  940  887  834  781 

.468  .883  728  676  623  570  517  463  410  357  304  251 

.469  198  145  092  039  986  932  879  826  773  720 

.470  .882  666  613  560  507  453  400  347  293  240  187 

.471  133  080  026  973  920  866  813  759  706  652 

.472  .881  599  545  491  438  384  331  277  223  170  116 

.473  062  009  955  901  848  794  740  686  632  579 

.474  .880  525  471  417  363  309  256  202  148  094  040 

.475  .879  986  932  878  824  770  716  662  608  554  499 

.476  445  391  337  283  229  174  120  066  012  958 

.477  .878  903  849  795  740  686  632  577  523  469  414 

.478  360  305  251  197  142  088  033  979  924  869 

.479  .877  815  760  706  651  597  542  487  433  378  323 

.480  268  214  159  104  050  995  940  885  830  775 

.481  .876  721  666  611  556  501  446  391  336  281  226 

.482  171  116  061  006  951  896  841  786  731  676 

.483  .875  620  565  510  455  400  344  289  234  1,79  123 

.484  068  013  957  902  847  791  736  680  625  570 

.485  .874  514  459  403  348  292  237  181  126  070  014 

.486  .873  959  903  848  792  736  681  625  569  513  458 

.487  402  346  290  235  179  123  067  Oil  955  900 

.488  .872  844  788  732  676  620  564  508  452  396  340 

.489  284  228  172  116  059  003  947  891  835  779 

.490  .871  722  666  610  554  497  441  385  329  272  216 

.491  160  103  047  990  934  878  821  765  708  652 

.492  .870  595  539  482  426  369  312  256  199  143  086 

.493  029  973  916  859  803  746  689  632  576  519 

.494  .869  462  405  348  291  235  178  121  064  007  950 

.495  .868  893  836  779  722  665  608  551  494  437  380 

.496  323  265  208  151  094  037  980  922  865  808 

.497  .867  751  693  636  579  521  464  407  349  292  234 

.498  177  120  062  005  947  890  832  775  717  660 

.499  .866  602  544  487  429  372  314  256  199  141  083 

.500  025  968  910  852  794  737  679  621  563  505 

(16) 


Table  I.     Values  of  ^/l^^ 


r  0  1234S6789 

.500  .866  025  968  910  852  794  737  679  621  563  505 

.SOI  .865  447  389  331  274  216  158  100  042  984  926 

.302  .864  868  810  752  693  635  577  519  461  403  345 

.503  286  228  170  112  053  995  937  879  820  762 

.504  .863  704  645  587  529  470  412  353  295  236  178 

.505  119  061  002  944  885  827  768  709  651  592 

.506  .862  533  475  416  357  299  240  181  122  064  005 

.507  .861  946  887  828  770  711  652  593  534  475  416 

.508  357  298  239  180  121  062  003  944  885  826 

.509  .860  767  707  648  589  530  471  411  352  293  234 

.510  174  115  056  996  937  878  818  759  700  640 

.511  .859  581  521  462  402  343  283  224  164  105  045 

.512  .858  985  926  866  807  747  687  628  568  508  448 

.513  389  329  269  209  149  090  030  970  910  850 

.514  .857  790  730  670  610  550  490  430  370  310  250 

.515  190  130  070  010  950  890  829  769  709  649 

.516  .856  589  528  468  408  347  287  227  167  106  046 

.517  .855  985  925  865  804  744  683  623  562  502  441 

.518  381  320  259  199  138  078  017  956  896  835 

.519  .854  774  714  653  592  531  470  410  349  288  227 

.520  166  105  044  984  923  862  801  740  679  618 

.521  .853  557  496  435  373  312  251  190  129  068  007 

.522  .852  945  884  823  762  701  639  578  517  455  394 

.523  333  271  210  149  087  026  964  903  841  780 

.524  .851  718  657  595  534  472  410  349  287  226  164 

.525  102  041  979  917  855  794  732  670  608  546 

.526  .850  485  423  361  299  237  175  113  051  989  927 

.527  .849  865  803  741  679  617  555  493  431  369  307 

.528  244  182  120  058  996  933  871  809  746  684 

.529  .848  622  559  497  435  372  310  248  185  123  060 

.530  .847  998  935  873  810  748  685  622  560  497  434 

.531  372  309  246  184  121  058  996  933  870  807 

.532  .846  744  682  619  556  493  430  367  304  241  178 

.533  115  052  989  926  863  800  737  674  611  548 

.534  .845  484  421  358  295  232  168  105  042  979  915 

.535  .844  852  789  725  662  599  535  472  408  345  281 

.536  218  154  091  027  964  900  837  773  710  646 

.537  .843  582  519  455  391  327  264  200  136  072  009 

.538  .842  945  881  817  753  689  626  562  498  434  370 

.539  306  242  178  114  050  986  922  857  793  729 

.540  .841665  601  537  472  408  344  280  215  151  087 

.541  023  958  894  830  765  701  636  572  507  443 

.542  .840  378  314  249  185  120  056  991  927  862  797 

.543  .839  733  668  603  539  474  409  344  280  215  150 

.544  085  020  956  891  826  761  696  631  566  501 

.545  .838  436  371  306  241  176  111  046  981  915  850 

.546  .837  785  720  655  590  524  459  394  329  263  198 

.547  133  067  002  937  871  806  740  675  609  544 

.548  .836  478  413  347  282  216  151  085  019  954  888 

.549  .835  822  757  691  625  559  494  428  362  296  231 

.550  165  099  033  967  901  835  769  703  637  571 

(17) 


Table  I.    Values  of  \fU^ 


r 


0  123456789 


.SSO  .835  165  099  033  967  901  835  769  703  637  571 

.SSI  .834  505  439  373  307  241  175  109  043  976  910 

.SS2  .833  844  778  712  645  579  513  447  380  314  248 

.553  181  115  048  982  916  849  783  716  650  583 

,SS4  .832  517  450  384  317  250  184  117  050  984  917 

.SSS  .831  850  784  717  650  583  517  450  383  316  249 

.SS6  182  115  048  982  915  848  781  714  647  580 

.SS7  .830  512  445  378  311  244  177  110  043  975  908 

.SS8  .829  841  774  706  639  572  505  437  370  302  235 

.559  168  100  033  965  898  830  763  695  628  560 

.560  .828  493  425  357  290  222  154  087  019  951  884 

.561  .827  816  748  680  612  545  477  409  341  273  205 

.562  137  069  001  933  865  797  729  661  593  525 

.563  .826  457  389  321  252  184  116  048  980  911  843 

.564  .825  775  706  638  570  501  433  365  296  228  159 

.565  091  022  954  885  817  748  680  611  543  474 

.566  .824  405  337  268  199  130  062  993  924  855  787 

.567  .823  718  649  580  511  442  373  304  236  167  098 

.568  029  960  890  821  752  683  614  545  476  407 

.569  .822  338  268  199  130  061  991  922  853  783  714 

.570  .821  645  575  506  436  367  298  228  159  089  020 

.571  .820  950  880  811  741  672  602  532  463  393  323 

,572  254  184  114  044  975  905  835  765  695  625 

.573  .819  555  485  415  346  276  206  136  066  995  925 

.574  .818  855  785  715  645  575  505  434  364  294  224 

.575  153  083  013  942  872  802  731  661  591  520 

.576  .817  450  379  309  238  168  097  027  956  885  815 

.577  .816  744  673  603  532  461  391  320  249  178  108 

.578  037  966  895  824  753  682  611  541  470  399 

.579  .815  328  257  185  114  043  972  901  830  759  688 

.580  .814  616  545  474  403  332  260  189  118  046  975 

.581  .813  904  832  761  689  618  546  475  403  332  260 

.582  189  117  046  974  902  831  759  687  616  544 

.583  .812  472  400  329  257  185  113  041  969  898  826 

.584  .811  754  682  610  538  466  394  322  250  178  105 

.585  033  961  889  817  745  672  600  528  456  383 

.586  .810  311  239  166  094  022  949  877  804  732  659 

.587  .809  587  514  442  369  297  224  152  079  006  934 

.588  .808861  788  716  643  570  497  424  352  279  206 

.589  133  060  987  914  841  768  695  622  549  476 

.590  .807  403  330  257  184  111  038  964  891  818  745 

.591  .806  672  598  525  452  378  305  232  158  085  Oil 

.592  .805  938  864  791  718  644  570  497  423  350  276 

.593  202  129  055  981  908  834  760  686  613  539 

.594  .804  465  391  317  243  170  096  022  948  874  800 

.595  .803  726  652  578  504  429  355  281  207  133  059 

.596  .802  984  910  836  762  687  613  539  464  390  316 

.597  241  167  092  018  943  869  794  720  645  571 

.598  .801  496  421  347  272  198  123  048  973  899  824 

.599  .800  749  674  599  525  450  375  300  225  150  075 

.600  000  925  850  775  700  625  550  475  399  324 

(18) 


Table  I.    Values  of  VT^? 

T  0  1234S6789 

.600  .800  000  925  850  775  700  625  550  475  399  324 

,601  .799  249  174  099  023  948  873  797  722  647  571 

.602  .798  496  421  345  270  194  119  043  968  892  817 

.603  .797  741  666  590  514  439  363  287  212  136  060 

.604  .796  984  909  833  757  681  605  529  453  377  301 

.605  225  149  073  997  921  845  769  693  617  541 

.606  .795  465  388  312  236  160  083  007  931  855  778 

.607  .794  702  625  549  473  396  320  243  167  090  014 

.608  .793  937  860  784  707  631  554  477  400  324  247 

.609  170  093  017  940  863  786  709  632  555  478 

.610  .792  401  324  247  170  093  016  939  862  785  708 

.611  .791  631  553  476  399  322  244  167  090  012  935 

.612  .790  858  780  703  626  548  471  393  316  238  160 

.613  083  005  928  850  772  695  617  539  462  384 

.614  .789  306  228  150  073  995  917  839  761  683  605 

.615  .788  527  449  371  293  215  137  059  981  903  824 

.616  .787  746  668  590  511  433  355  277  198  120  042 

.617  .786  963  885  806  728  649  571  492  414  335  257 

.618  178  099  021  942  863  785  706  627  549  470 

.619  .785  391  312  233  154  076  997  918  839  760  681 

.620  .784  602  523  444  365  286  206  127  048  969  890 

.621  .783  811  731  652  573  493  414  335  255  176  097 

.622  017  938  858  779  699  620  540  461  381  301 

.623  .782  222  142  063  983  903  823  744  664  584  504 

.624  .781424  344  265  185  105  025  945  865  785  705 

.625  .780  625  545  465  384  304  224  144  064  984  903 

.626  .779  823  743  662  582  502  421  341  261  180  100 

.627  019  939  858  778  697  617  536  455  375  294 

.628  .778  213  133  052  971  890  810  729  648  567  486 

.629  .777  405  324  243  162  081  000  919  838  757  676 

.630  .776  595  514  433  352  270  189  108  027  945  864 

.631  .n^lSZ  701  620  539  457  376  294  213  131  050 

.632  .774  968  887  805  724  642  560  479  397  315  234 

.633  152  070  988  906  825  743  661  579  497  415 

.634  .773  333  251  169  087  005  923  841  759  676  594 

.635  .772  512  430  348  265  183  101  019  936  854  771 

.636  .771  689  607  524  442  359  277  194  112  029  946 

.637  .770  864  781  698  616  533  450  368  285  202  119 

.638  036  953  871  788  705  622  539  456  373  290 

.639  .769  207  124  041  957  874  791  708  625  541  458 

.640  .768  375  292  208  125  042  958  875  791  708  624 

.641  .767  541  457  374  290  207  123  039  956  872  788 

.642  .766  705  621  537  453  370  286  202  118  034  950 

.643  .765  866  782  698  614  530  446  362  278  194  110 

.644  025  941  857  773  689  604  520  436  351  267 

.645  .764  183  098  014  929  845  760  676  591  507  422 

.646  .763  337  253  168  083  999  914  829  744  660  575 

.647  .762  490  405  320  235  150  065  980  895  810  725 

.648  .761  640  555  470  385  300  215  129  044  959  874 

.649  .760  788  703  618  532  447  362  276  191  105  020 

.650  .759  934  849  763  678  592  506  421  335  249  163 

(19) 


Table  L     Values  of  Vl^=? 

r  0               123456789 

.6S0  .759  934  849  763  678  592  506  421  335  249  163 

.651  078  992  906  820  734  649  563  477  391  305 

.652  .758  219  133  047  961  875  789  703  616  530  444 

.653  .757  358  272  185  099  013  927  840  754  667  581 

.654  .756  495  408  322  235  149  062  975  889  802  716 

.655  .755  629  542  455  369  282  195  108  022  935  848 

.656  .754  761  674  587  500  413  326  239  152  065  978 

.657  .753  891  803  716  629  542  455  367  280  193  105 

.658  018  931  843  756  668  581  493  406  318  231 

.659  .752  143  055  968  880  792  705  617  529  441  353 

.660  .751  266  178  090  002  914  826  738  650  562  474 

.661  .750  386  298  210  122  033  945  857  769  680  592 

.662  .749  504  415  327  239  150  062  973  885  796  708 

.663  .748  619  531  442  354  265  176  088  999  910  821 

.664  .747  733  644  555  466  377  288  199  110  021  932 

.665  .746  843  754  665  576  487  398  309  219  130  041 

.666  .745  952  862  773  684  594  505  416  326  237  147 

.667  058  968  879  789  699  610  520  430  341  251 

.668  .744  161  071  982  892  802  712  622  532  442  352 

.669  .743  262  172  082  992  902  812  722  632  542  451 

.670  .742  361  271  181  090  000  910  819  729  638  548 

.671  .741  457  367  276  186  095  005  914  823  733  642 

.672  .740  551  460  370  279  188  097  006  915  824  733 

.673  .739  642  551  460  369  278  187  096  005  914  823 

.674  .738  731  640  549  458  366  275  183  092  001  909 

.675  .737  818  726  635  543  452  360  268  177  085  993 

.676  .736  902  810  718  626  534  443  351  259  167  075 

.677  .735  983  891  799  707  615  523  431  339  246  154 

.678  062  970  877  785  693  600  508  416  323  231 

.679  .734  138  046  953  861  768  676  583  490  398  305 

.680  .733  212  119  027  934  841  748  655  562  469  376 

.681  .732  283  190  097  004  911  818  725  632  539  445 

.682  .731  352  259  166  072  979  886  792  699  605  512 

.683  .730  418  325  231  138  044  951  857  763  669  576 

.684  .729  482  388  294  201  107  013  919  825  731  637 

.685  .728  543  449  355  261  167  073  978  884  790  696 

.686  .727  602  507  413  319  224  130  035  941  846  752 

.687  .726  657  563  468  374  279  184  090  995  900  805 

.688  .725  711  616  521  426  331  236  141  046  951  856 

.689  .724  761  666  571  476  381  286  190  095  000  905 

.690  .723  809  714  619  523  428  332  237  141  046  950 

.691  .722  855  759  664  568  472  376  281  185  089  993 

.692  .721  897  802  706  610  514  418  322  226  130  034 

.693  .720  938  841  745  649  553  457  360  264  168  071 

.694  .719  975  879  782  686  589  493  396  300  203  106 

.695  010  913  816  720  623  526  429  332  236  139 

.696  .718  042  945  848  751  654  557  460  363  265  168 

.697  .717  071  974  877  779  682  585  487  390  293  T95 

.698  .716  098  000  903  805  708  610  512  415  317  219 

.699  .715  122  024  926  828  730  633  535  437  339  241 

.700  .714  143  045  947  849  751  652  554  456  358  260 

(20) 


Table  I.    Values  of  VT^=P 


r                0  12  3  4               S  6          7         8  9 

.700  .714  143  045  947  849  751  .713  652  554  456  358  260 

.701  .713  161  063  965  866  768  .712669  571  473  374  276 

.702  .712  177  078  980  881  782  .711684  585  486  387  289 

,703  ,711190  091  992  893  794  .710695  596  497  398  299 

.704  .710  200  101  002  902  803  .709  704  605  505  406  307 

.705  .709  207  108  008  909  809  .708  710  610  511  411  312 

.706  .708  212  112  012  913  813  .707  713  613  513  413  314 

.707  .707  214  114  014  914  813  .706  713  613  513  413  313 

.708  .706  212  112  012  912  811  .705  711  610  510  409  309 

.709  .705  208  108  007  907  806  .704  705  605  504  403  302 

.710  .704  202  101  000  899  798  .703  697  596  495  394  293 

.711  .703  192  091  990  889  787  .702  686  585  484  382  281 

.712  .702  179  078  977  875  774  .701672  571  469  367  266 

.713  .701164  062  961  859  757  .700  655  553  452  350  248 

.714  .700  146  044  942  840  738  .699  635  533  431  329  227 

.715  .699  124  022  920  818  715  .698  613  510  408  305  203 

.716  .698  100  998  895  792  690  .697  587  484  382  279  176 

.717  .697  073  970  867  764  661  .696  559  455  352  249  146 

.718  .696  043  940  837  734  630  .695  527  424  320  217  114 

.719  .695  010  907  803  700  596  .694  492  389  285  182  078 

.720  .693  974  870  767  663  559  .693  455  351  247  143  039 

.721  .692  935  831  727  623  519  .692  414  310  206  102  997 

.722  .691893  789  684  580  475  .691371  266  162  057  953 

.723  .690  848  743  639  534  429  .690  324  220  115  010  905 

.724  .689  800  695  590  485  380  .689  275  170  065  959  854 

.725  .688  749  644  538  433  328  .688  222  117  Oil  906  800 

.726  .687  695  589  483  378  272  .687  166  061  955  849  743 

.727  .686  637  532  426  320  214  .686  108  002  896  789  683 

.728  .685  577  471  365  258  152  .685  046  939  833  727  620 

.729  .684  514  407  301  194  087  .683  981  874  767  661  554 

.730  .683  447  340  233  127  020  .682  913  806  699  592  485 

.731  .682  377  270  163  056  949  .681841  734  627  519  412 

.732  .681305  197  090  982  875  .680  767  659  552  444  336 

.733  .680  229  121  013  905  797  .679  689  582  474  366  258 

.734  .679  149  041  933  825  717  .678  609  500  392  284  175 

.735  .678  067  959  850  742  633  .677  525  416  308  199  090 

.736  .676  982  873  764  655  546  .676  438  329  220  111  002 

.737  .675  893  784  675  565  456  .675  347  238  129  019  910 

.738  .674  801  691  582  472  363  .674  253  144  034  925  815 

.739  .673  705  596  486  376  266  .673  157  047  937  827  717 

.740  .672  607  497  387  277  167  .672  056  946  836  726  615 

.741  .671505  395  284  174  063  .670  953  842  732  621  511 

.742  .670  400  289  178  068  957  .669  846  735  624  513  402 

.743  .669  291  180  069  958  847  .668  736  625  514  402  291 

.744  .668  180  068  957  845  734  .667  622  511  399  288  176 

.745  .667  064  953  841  729  617  .666  506  394  282  170  058 

.746  .665  946  834  722  610  498  .665  385  273  161  049  936 

.747  .664  824  712  599  487  374  .664  262  149  037  924  811 

.748  .663  699  586  473  360  248  .663  135  022  909  796  683 

.749  .662  570  457  344  231  118  .662  004  891  778  665  551 

.750  .661438  324  211  098  984  .660  870  757  643  530  416 

(21) 


Table  I.    Values  of  \/T=I^ 


r  0  12  3  4  S  6  7  8  9 

.750      .661438      324      211      098      984      .660  870  757  643  530  416 

.659  733  619  505  391  277 

.658  592  478  364  249  135 

.657  448  333  219  104  989 

.656  300  185  070  955  840 

.655  149  033  918  803  687 

.653  994  878  762  647  531 

.652  835  719  603  487  371 

.651  673  557  440  324  207 

.650  507  391  274  157  040 

.649  338  221  104  986  869 

.648  165  047  930  812  695 

.646  988  870  752  634  517 

.645  808  690  571  453  335 

.644  624  505  386  268  149 

.643  436  317  198  079  960 

.  642  244  125  006  886  767 

.641  049  929  809  690  570 

.639  850  730  609  489  369 

.  638  647  526  406  285  165 

.637  440  319  198  077  956 

.  636  229  108  987  865  744 

.635  015  893  771  650  528 

.  633  796  674  552  430  308 

.632  574  451  329  206  084 

.631  348  225  102  979  856 

.630  117  994  871  747  624 

.628  883  759  636  512  388 

.627  645  521  396  272  MS 

.626  402  278  153  029  904 

.625  156  031  906  781  656 

.623  905  780  655  529  404 

.622  651  525  399  273  148 

.621  392  266  140  013  887 

.620  129  002  876  749  622 

.618  862  735  608  481  354 

.617  590  463  335  208  081 

.616  315  187  059  931  803 

.615  035  907  778  650  522 

.613  751  622  493  364  236 

.612  462  333  204  075  945 

.611  169  040  910  780  651 

.609  872  742  612  482  352 

.  608  570  440  309  179  048 

.607  264  133  002  871  740 

.605  954  822  691  560  428 

.604  639  507  375  243  ni 

.603  319  187  054  922  790 

.601  995  862  729  597  464 

,600  666  533  400  267  133 

.599  333  199  066  932  798 


751 

.660  302 

189 

075 

961 

847 

752 

.659  163 

049 

935 

821 

706 

753 

.658  021 

906 

792 

677 

562 

754 

.656  874 

760 

645 

530 

415 

755 

.655  725 

610 

494 

379 

264 

756 

.654  572 

456 

341 

225 

109 

757 

.653  415 

299 

183 

067 

951 

758 

.652  255 

138 

022 

906 

789 

759 

.651  091 

974 

857 

741 

624 

760 

.649  923 

806 

689 

572 

455 

761 

.  648  752 

635 

517 

400 

282 

762 

.647  577 

459 

342 

224 

106 

763 

.646  398 

280 

162 

044 

926 

764 

.645  216 

098 

979 

861 

742 

765 

.  644  030 

911 

793 

674 

555 

766 

.642  841 

721 

602 

483 

364 

767 

.641  647 

528 

408 

288 

169 

768 

.640  450 

330 

210 

090 

970 

769 

.639  249 

128 

008 

888 

767 

770 

.  638  044 

923 

802 

682 

561 

771 

.636  835 

714 

593 

472 

351 

772 

.635  623 

501 

380 

258 

136 

773 

.  634  406 

284 

162 

040 

918 

774 

.633  186 

063 

941 

819 

696 

775 

.631  961 

839 

716 

593 

470 

776 

.630  733 

610 

487 

364 

240 

777 

.629  501 

377 

254 

130 

007 

778 

.628  264 

140 

017 

893 

769 

779 

.627  024 

900 

775 

651 

527 

780 

.625  780 

655 

530 

405 

281 

781 

.624  531 

406 

281 

156 

030 

782 

.623  278 

152 

027 

902 

776 

783 

.622  022 

896 

770 

644 

518 

784 

.620  761 

635 

508 

382 

255 

785 

.619  496 

369 

242 

115 

989 

.786 

.618  226 

099 

972 

845 

718 

.787 

.616  953 

825 

698 

570 

442 

,788 

.615  675 

547 

419 

291 

163 

.789 

.614  393 

265 

136 

008 

879 

.790 

.613  107 

978 

849 

720 

591 

.791 

.611  816 

687 

557 

428 

299 

.792 

.610521 

391 

262 

132 

002 

.793 

.609  222 

091 

961 

831 

701 

.794 

.607  918 

787 

656 

526 

395 

.795 

.606  609 

478 

347 

216 

085 

.796 

.605  297 

165 

034 

902 

770 

.797 

.603  979 

847 

715 

583 

451 

.798 

.602  657 

525 

393 

260 

127 

.799 

.601  331 

198 

065 

932 

799 

.800 

.  600  000 

867 

733 

600 

466 

(22) 

Table  I.     Values  of  VI — *" 


r       0  12          3  4                5              6  7          8  9 

.800  .600  000  867  733  600  466  .599  333  199  066  932  798 

.801  .598  664  531  397  263  129  .597  995  861  727  592  458 

.802  .597  324  190  055  921  787  .596  652  518  383  248  114 

.803  .595  979  844  709  575  440  .595  305  170  035  900  764 

.804  .594  629  494  359  223  088  .593  953  817  682  546  410 

.805  .593  275  139  003  868  732  .592  596  460  324  188  052 

.806  .591  916  779  643  507  370  .591  234  098  961  825  688 

.807  .590  551  415  278  141  004  .589  868  731  594  457  320 

,808  .589  182  045  908  771  634  .588  496  359  221  084  946 

.809  .587  809  671  533  396  258  .587  120  982  844  706  568 

.810  .586  430  292  154  015  877  .585  739  600  462  323  185 

.811  .585  046  908  769  630  491  .584  352  214  075  936  797 

.812  .583  657  518  379  240  101  .582  961  822  682  543  403 

.813  .582  264  124  984  845  705  .581565  425  285  145  005 

.814  .580  865  725  584  444  304  .580  164  023  883  742  602 

.815  .579  461  320  180  039  898  .578  757  616  475  334  193 

.816  .578  052  911  769  628  487  .577  345  204  062  921  779 

.877  .576  638  496  354  212  071  .575  929  787  645  503  360 

.818  .575  218  076  934  791  649  .574  507  364  221  079  936 

.819  .573  794  651  508  365  222  .573  079  936  793  650  507 

.820  .572  364  220  077  933  790  .571647  503  359  216  072 

.821  .570  928  784  640  497  353  .570  209  064  920  776  632 

.822  .569  487  343  199  054  910  .568  765  620  476  331  186 

.823  .568  041  896  751  606  461  .567  316  171  026  881  735 

.824  .566  590  444  299  153  008  .565  862  716  570  425  279 

.825  .565  133  987  841  695  548  .564  402  256  109  963  817 

.826  .563  670  524  377  230  084  .562  937  790  643  496  349 

.827  .562  202  055  908  760  613  .561466  318  171  023  876 

.828  .560  728  580  433  285  137  .559  989  841  693  545  397 

.829  .559  249  100  952  804  655  .558  507  358  210  061  912 

.830  .557  763  615  466  317  168  .557  019  869  720  571  422 

.831  .556  272  123  974  824  674  .555  525  375  225  075  926 

.832  .554  776  626  476  325  175  .554  025  875  724  574  424 

.833  .553  273  122  972  821  670  .552  519  369  218  067  916 

.834  .551  764  613  462  311  159  .551  008  856  705  553  402 

.835  .550  250  098  946  794  642  .549  490  338  186  034  882 

.836  .548  729  577  425  272  120  .547  967  814  661  509  356 

.837  .547  203  050  897  744  591  .546  437  284  131  977  824 

,838  .545  670  517  363  209  055  .544  902  7^48  594  440  286 

.839  .544  131  977  823  669  514  .543  360  205  051  896  741 

.840  .542  586  432  277  122  967  .541812  656  501  346  191 

.841  .541035  880  724  569  413  .540  257  101  945  790  634 

.842  .539  478  321  165  009  853  .538  696  540  383  227  070 

.843  .537  914  757  600  443  286  .537  129  972  815  658  501 

.844  .536  343  186  028  871  713  .535  556  398  240  082  924 

.845  .534  766  608  450  292  134  .533  975  817  659  500  342 

,846  .533  183  024  865  707  548  .532  389  230  071  911  752 

,847  .531593  434  274  115  955  .530  795  636  476  316  156 

,848  .529  996  836  676  516  356  .529  195  035  875  714  553 

,849  .528  393  232  071  911  750  .527  589  428  266  105  944 

.850  .526  783  621  460  298  137  .525  975  813  652  490  328 

(23) 


•^  Pfl  <*1  ^  ws 
U5  Ift  Ift  UJ  VJ 

00  00  00  00  00 


<oKooos©     •««^^^5^«fl 

W5U5«fllO<0       ;o  «e  «c  <o  to 

QOOOOOQOOO        OOOQOOQOOO 


to  N.  00  0)0 

to  to  to  to  N 

00  00  CO  00  00 


K  (v  K  S,  K 

00  00  00  00  00 


0> 


^  rf  r^  PI  <-i 

o  r*  «  o>  t 

t*  O  Tj"  t>.  -< 

CO  N  o  00  r^ 

N  N  N  1-1  —> 

10 10  in  10  u) 


cj  t^  w  CO  'i' 

00  ^•^  tc  r^ 

Tf  00  •I  ^  t^ 

to  n  N  o  00 
i-<  1^  t^  t-»  o 
lOlO  lO  lO  lO 


00  in  CO  ^  t» 
r*  t^  to  ^  .- 

O  CO  to  0>  N 

r»  in  M  >-i  o 
o  oo  o  o 
10 10  in  to  in 


N  0)  QOOOO 
00  rO  00  N  to 

00  to  ^  M  i-i 
O)  0>  O)  O)  0) 

"(f  ^  ^  ^  'tj' 


^  o)  to  ^  CO 
00  O)  o  o  o> 

to  00  <-»  CO  ^ 
Oi  t*  to  ^  N 

00  00  W  CO  00 
^  ^  ^  ^  ^ 


r>>  00  '-'  CO  t* 
to  M  o  in  o 
00  N  ;o  0>  ro 

M  N  O  00  t* 
N  N  N  i-H  rt 

10  in  in  in  in 


Oi  ^  •^  <-  M 
^  00  i-<  CO  ^ 

to  ff>  CO  too 

10  CO  N  O  00 

«-<  1^  ^H  »^  O 

in  in  in  in  in 


00  in  in  to  o 

^  ^  CO  »^  Ci 

N  in  00  t-1  CO 
r^  in  CO  M  o 
o  o  o  o  o 
in  in  in  in  in 


tO'^  CO  Tf  t^ 
lO  f-c  to  O  CO 

to  05  »-"  ^  to 

00  to  in  CO  ^ 

0>  05  O)  05  0) 
rj"  Tl"  Tf  ^  It 


N  ooin^  ^ 

to  r^  00  00  r« 
00  O  CM  ^  w 

Oi  00  tO't  CM 
00  00  CO  00  00 
^  ^  ^  "^  ^ 


O  f-i  ION  CM 

CO  o  to  N  r^ 
o  t  r^  •-'  t 

■^  M  O  OJN. 
N  CM  CM  <-"  1-1 

lo  10  10  loin 


in  o  OiO)  CM 
1-1  in  r*  o>  i-i 

00  l->  Tj-  1^  l-l 

in^j"  CM  o  05 

l-M  fl-H  1-^  ^H  O 

mm  in  10 lo 


00  to  to  05  CO 

i->  ^  O  00  to 

•^r^  o  cMm 
t^m  ^  CM  o 

o  o  o  oo 


o  00  05  fim 

CO  00  CO  00  i-< 

00  o  ro  m  00 
00  r^m  CO  1-1 

0)  05  05  05  05 

^  ^  ^  ^  ^ 


o  r^mm  to 

^m  to  to  m 

O  CM  ^  to  00 
O  00  to  ^  CM 
05  00  00  00  CO 
^^  Tf  Tt  ^ 


to 


CM  >*  05  t*00 

05  to  CM  CO  CO 
T->m05  CM  to 
t  CMO  0>I^ 
CM  CM  CM  1-1  1-1 


i-«  t^  tOOO  1-1 
00  1-1^  to  00 
0)  CO  to  05  CM 

m^  c«)o  05 

r^  1-M  1^  1-N  O 

mmmm  m 


00  t*  00  1-1  to 
00  00  r*  to  CO 
m  00  1-1 1  r^ 
r*  m  t  CM  o 

O  O  OO  o 

m  mm  mm 


COCO^  t*CM 

o  to  1-1  m  o5 

O  CM  m  t^05 

05  t*m  coi-i 

05  05  05  05  05 
^  ^  ^  ^  ^ 


00  tomm  t^ 

•^  CO  ^  Tj"  CO 

CM  Tr  to  «  o 
o  00  to^  ro 

05  00  CO  00  00 
^•^rf  Tt  ^ 


> 


en 

> 


«n 


m  1^  CO  1-1  CO 

m  CM  o5  m  o 
CO  r^  o  ^  00 

Tj"  CM  1-1  05  tN. 
CM  CM  CM  1-1  i-« 

mmm  m  m 


r^  '^  ^  too 
Tf  00 1-1  CO  m 

1-1  ^  00  1-1  ^ 
to  ^  CM  1-1  05 
I— (  1^  rri  r^  O 

m  mmmm 


00  f^  05  CO  05 

m  m  t  CO  o 
t^  o  ro  CO  05 

i^to  rf  c«j  o 
o  o  oo  o 
mm  m  m  m 


t*  l>»  05  CO  00 

r^  CO  00  CO  to 

1-1  ^  to  05  1-1 

ovr^mcocM 

05  05  05  05  05 
^  ^  ^  ^  ^ 


to^Tt  tooo 

05  ^  C>J  CM  -N 
CO  to  «  O  CM 

o  00  torn  CO 

O)  00  00  00  00 


t^  O  1^  (O  00 

,H  05  m  rH  to 
in  00  CM  ;o  o 

Tj-  CM  1^  05  t* 
MCMCM  rH-H 

m  inmmm 


CO  1^  1-"  'i'  05 
rH  m  00  O  1-1 
CO  to  05  CO  to 
tC*  CM  T-1  05 

»-i  iM  i-H  1-1  o 

mmmm  m 


t^iN.o  mcM 

CM  CM  CM  O  « 

05  cMm  00  o 

r^  tOrf  CM  rt 
O  OOO  o 

mmmm  m 


1-1  CM  ^  05m 

m  1-1  to  o  ^ 

CO  to  00  1-1  CO 

o>  r«-m  Tf  CM 

05  05  05  05  05 

^  ^  ^  ^  ^ 


CO  CO  ^  to  05 
t«  05  O  O  05 

m  t^  o  CM  CO 

o  CO  r^m  CO 

05  00  00  00  00 


H 


05  CO  O  O  CO 

t«m  CM  00  CO 

;e  o  ^  i^  "-■ 

^  CO  1-1  05  00 
M  M  M  1-1  .-1 

m>om  mm 


05  t«  00  CM  00 
I^  1-1  ^  t^  00 

Tf  00  1-1  >*  r>. 

to  ^  CO  1^  05 
1-^  1-1  1-^  1-^  O 

mmmmm 


t^ooii  r^"* 

05  05  05  r^m 

O  CO  to  05  M 
00  to  ^  CM  1-1 
O  O  O  OO 

mmmmm 


rf  to  OsmCM 
CM  00  CO  00  CM 

m  t«o  Mm 

05t^  to  Tf  CM 

05  05  05  05  05 
^  ^  ^  ^  ^ 


•-1  f-  CO  to  O 

m  t^  00  00  00 
t»05 1-1  CO  m 

o  00  t«m  CO 

0>  00  00  00  00 

>*  t  TJl  ^  'S* 


M 


fM  to^moo 

^  1-1  CO  ^  05 
00  CM  m  05  N 
Tt  CO  1-1  05  00 
CM  CM  CM  1-1  1-1 

in  m  m  m  lo 


m  ^mo  t* 

Tj-  00  1-1  "<t  m 

to  05  CO  to  05 

to  Tf  CO  1-1  05 
1^  i-i  i-i  ,-■  o 

mmmmm 


CO  00  CM  00  r« 

to  to  to  ^  CM 

CM  moo  1-1  ^ 

00  to  ^  CO  ^ 

o  o  o  o  o 
mmmmm 


t*  o  ^  i-<  o> 

05  to  ^  to  05 
to  05  CM  Tf  O 
0»r*tO  t  CM 
05  05  05  05  05 

^  ^  Xj*  ^  ^ 


00O5M  tOfi 
CM  ^  to  to  to 

05 1-1  CO  m  r* 
o  05 1^  m  CO 

05  00  00  00  00 
^  ^  ^  ^  ^ 


^  05  r*  C5  CO 

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to  0)  O  0)  CO 

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to  t^  00  O)  o 
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(26) 


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in  to  coin  (4 

to  r^  CO  M  to 

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N  t»M  OOCO 

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05  CO  to  00  t^ 
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to  to  in  m  m 

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CO  to  in  oo 

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in  ^  ^  Tf  CO 

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in  ^  o  CO  ^ 

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to  CO  o  r*  in 

CO  CO  COCVI  N 

CO  CO  CO  CO  CO 


r>.  CO  00  i-iM 

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4) 

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00  in  C4  o  00 
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to  CO  1-1  00  to 
r^  t»  r«  to  to 
CO  CO  CO  CO  CO 


10  N  r«.o  N 

00  I-I  ^  o  to 

'i'  05  CO  h-  O 

CO  o  00  in  CO 
to  CO  in  in  in 

CO  CO  CO  CO  CO 


o  to  h«int« 

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Tf  N.  OM  in 

o  t«in  N  05 

in  ^  ^  rt  CO 

CO  CO  CO  CO  CO 


CO  t  CO  Tj^M 

coe^  00  M  CO 
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toco  <-i  00  in 

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CO  CO  CO  CO  CO 


O  05  00  ^  00 

IX  in  t*  C0 11 

^  ^  ^  ^  ^ 
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CO  CO  CO  CO  CO 


inco  NM  M 
05  CM  COM  05 
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to  CO  1-1  00  to 

t^  r*  r^  CO  to 

CO  CO  CO  CO  CO 


«-"  o  t*  CO  r^ 
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t*  i-<  in  05  CO 

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to  coioio  in 

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00  in  05  05  ^ 

to  00  t"-  ^  05 

to  05  M  in  t^ 

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in  t  Tf  It  CO 

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CO  tOCOi-iM 

^  o  r*  I-I  N 
o  Ncointo 
r*  ^  I-I  coin 

CO  CO  CO  M  M 
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rt  to  r^  r«in 
oin  r^  toM 
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M  05  to  coo 
M  I-I  n  f-<  n 
CO  CO  CO  CO  CO 


1-1  ^M  ^  to 
t  t^OO  t^it 

looiooin 

to  't  ii  05  CO 

h- 1*  r*  to  to 

CO  coco  coco 


r^  00  00  CO  ^ 

0>  M  CO  M  05 
05  ^  00  M  m 
CO  I-I  00  to  CO 

CO  CO  in  in  10 

CO  CO  CO  CO  CO 


lOin^  coo 
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in  ^  t  ^  t 

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05  00  in  05  •-• 
M  ^  to  t^05 

r*  ^  i-<  00  in 

CO  CO  CO  M  M 
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t^  M  to  05O 

cnin  t^co  CO 

0500  0  0 

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M  M  ^  <-i  1-1 
CO  CO  CO  CO  CO 


a 
H 


r*05M  too 

00  "-"CO  M  O 
t^  CO  00  CO  00 

CO  t  1-1  05  CO 

r^  t*  t»  CO  CO 

CO  CO  CO  CO  CO 


CO  to  00  00  to 

in  00  05  00  in 

M  too  ^  00 
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CO  to  mm  lo 

CO  CO  CO  CO  CO 


1-"  ■^M  r-r* 

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m  ^  't  t  It 
CO  CO  CO  coco 


nO  »-<  tOM 

t^  r*  t  00  o 
m  r>>  05  o  M 

r*  ^  1-1  o>  to 

CO  CO  CO  M  N 
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o  oom  M  to 

05  Tj"  t*  t>.  CO 
M  CO  CO  CO  CO 

CO  o  t>»  ^  I-I 

N  M  ^  i-iTH 
CO  CO  CO  CO  CO 


e«i 


CO  r*  M  i^co 

CO  CO  00  t^  m 
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05  t  t^o  o 
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m  05  CO  r^  I-I 

^  n  05  CO  ^ 

CO  to  m  m  m 

CO  CO  CO  CO  CO 


00  M  rf  ^  CO 
to  05  05  r^  M 

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m  ^  ^t  "<t  ^ 

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o  »Hm  CO  M 
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00  OM  CO^ 

t^m  M  05  to 

CO  CO  CO  N  M 
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M  CO  -t  CO  1-1 

00  ^  t^  r^^ 

in  CO  CO  CO  CO 
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N  M  I-I  i-H  n 

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00  ^  n  05  to 

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M  00  CO  00  CO 
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CO  CO  CO  CO  CO 


^  •-«  r*i-i  ^ 

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t*  M  CO  O  CO 

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to  to  m  m  m 

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^  1-im  t  05 

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m  ^  Tt  ^  ^ 

coco  coco  CO 


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CO  CO  CO  CO  CO 


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t«.  CO  t^  ^^  iij* 

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m  o  m  o  m 
t«m  N  o  r>- 

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05  00  CO  CO  00 

I-I  m  r«  r^  ^ 

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CO  CO  m  m  m 

CO  CO  CO  CO  CO 


oosm  r«^ 
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O  CO  to  05  •I 
M  05  CO  CO  1-1 

m  Tt  Tf  Tt  Tf 

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i<»co  CO  m  o 

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^  to  r^  05  o 
oom  M  05  r* 

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CO  CO  CO  CO  CO 


r^'t  o  too 
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1-1  M  M  N  M 

1 1-1  oom  M 
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e5       SmSSS       ISSJS2252       toN.00050       •^MCO'VWJ        COK00050 
05        0505O50505        05  05  05  Oi  Oi        95  05  05  05  (»        55555        5555S 


(27) 


Oi  06  A  0>  ^ 


(O  <0  (O  (O  (O 
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o>  in  10  CO  CM 

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50  toco  ^  in 
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in  <-i  r^  CO  oi 
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CM  CMN  CMCM 


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coin  CO  in  00 
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t.  1^  CO  CO  in 

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win  ^  ^  CO 

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t^  r*  C0 1-1  in 

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0  r^.'*  oin 
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01  00  00  00  1^ 
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^  ,-4  r»i-iO 
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r«  r«  CO  coin 

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M  in  Tf  oiin 

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00  CO  t  t*»-i 
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M  o  coin  1-1 

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M  MMM  N 


01  CO  CO  1-1  l>> 

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COM  O  00  CO 
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OO  O  Ol  Ol 
coco  COM  M 


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1-1 00  ^  »-i  r* 

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NMM  MM 


0  oo^inoo 

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MMM  M  M 


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CO 

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00 11 01 1-1  m 
in  in  o  CO  •"■ 
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MCOCOOlO 
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If  1-  !*•*  O 

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01  00  00  00  t» 
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CO  COM  r*  CO 
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H 


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to 


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CM  ^  to  CO  CO 

in  ^  00  r^  ^ 
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r«r*  to  to  to 

M  M  M  MM 


^  to  r»in  to 

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M  M  M  M  M 


CO  MO  COM 

to  in  CO  00  M 

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CO  r*  to  00  ^ 
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to  01  to  too 

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CO  t»  CO  00  CO 

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M  M  MM  M 


1-1  00  O  t^  CO 

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h- 00  00  coo 
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(28) 


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O)  0)  0>  0) 


t^  CO  O  A  CO 
0>  t^  't  00  »-■ 
O  O  CO  1*  U5 

CO  Oi  '!l'  Oi  ^ 
*-i  O  O  A  A 
MM  N  '-■i-i 


000'<t« 

o  ■'t  ^^  N  CO 

^  _  t".  tx  CO 
O)  rf  00  CO  t» 

00  00  r«i^(o 


codcot^o 

CO  O)  00  CO  o 
CO  O  U5  t*  «0 
t-i  to  00  1-"  ^ 
«DU5  ^  t  CO 


o 

.-iNUSCO^ 
M  U)  00  CO  CO 
O  0>M  OCt 

r«  eo  o  o  o 

M  .-«  t-iO  m 


O  ^  PI  00 

05  CO  i-i  "^ 

t^  t*  «  ^ 

CO  r*  00  »-i 

00  Tt  CO-* 

r^  CO  t  -* 
oooo 


^  o  00  o  CO 

U5  ^  1-.  00  ^ 

iM  in  00  o>o 
^  a>  ^  oi  in 

^O  00)0) 
N  N  esi  ^  »H 


OOCOO  M  •* 

•-I  t^  r*  o>  e>» 

O)  CO  M  CO  0> 
OJ  ^  ©  CO  t- 

00  00  r^  r«  CO 


"t  00  r>»^  ^ 
■<t  M  Tf  coco 
Oir^pi  •*  CO 

•-iin  9)  M  in 
cow'^'t  CO 


N 

o^coooin 
o  00  00  rt<  in 
00  r*  I-*  00  in 

r»  o>  »^  «-■  i^ 
e^  i-irio  O) 


Od-"© 

CO  coin  A 

CO  O)  h»  0> 
ACM  AO> 

O)  CO  00  0) 

r*  cott  -^ 
oooo 


A  CO  CO  A  A 
O  O  O)  co<-< 
CO  o  M  ^  in 
t  o  ino  in 

.-  r-lO  O  Oi 

C4C4  N  N  •>■ 


rrm  t»ooo 
«o  1-1  in  i-i 

^N  00  CM  in 

o  in  a>  ^  00 
ooo  t^  r^co 


N  i-r  00  t^  ^ 

in  CO  o  in  CO 
in  CO  oi  "-I  o 

M  CO  0)  CO  CO 

coin  ^•«r  CO 


coocooco 

t^  _!  t^  N  CO 

in  CO  ooo  CO 

00  O  M  N  N 

M  N  f-i  O  O) 
.-i^^^O 


CO  CO  CO  >-« 
CO  "^  CO  CO 

r^  00  h>  A 

i-<  h»  0>  Tf 

ri  r^  o  ^ 
00  com  N 
oooo 


« 


•^  1-1  e>i  r*  oj 
CO  r^  t^iOi-" 
o  't  t*  o>o 

to  o  in  o  CO 

^  t-iO  o  OJ 
N  C4  C4M  f^ 


0»^  tN  t 

^cocoeg  o> 

A  t^  CO  00  O 

oin  o  t  o» 
0)<o  00  t«co 


00  t-ico  ^»o 
in  A  CO  t  05 
ri  01  in  00  r^ 

CO  CO  O  CO  CO 

CO  to  in  ^  CO 


N  o  CO  CO  in 
^  CO  in  00  o 
CO  ^  o>  r^r* 

0>  rH  N  CO  CO 
N  M  1-4  O  O) 

^^^f^O 


oioin^ 

C4  O  CO  ^ 
O)  ^  O)  00 
COCM  OOM 

M  A  M  00 

00  CO  m  c<i 
oooo 


> 

Mm 
O 

S 

"(3 
> 


u> 


t»in  r*^  o> 

^^  n  ^  ^  y-t 
in  A  c^]  ^  in 

lOO  CO  ^co 

•-I  ri  O  O  0> 


OOO  «->ot* 

t^  Oi  CNl  CO  OH 

O)cot^a)0 
in  OH  CO  i-i  r« 

1-1  rl  o  oo> 
NNM  M  i-i 


N  CO  00  inm 
CO  CO  o  00  r« 

^  N  «C0  CO 
i->CO  O  lOO) 

0)00  00  1^  CO 


i-iO»«-iC0C0 
CO  FN  C>«  CO  <-■ 

r«  CO  P4  lo  lo 
CO  r*  .-I  •^  r* 
CO  lom  ^  CO 


to 
r»io  c>j  t^  t-i 

O  ^  CO  CO  CO 

1-1  N  «  r^  t* 

O  CM  CO  ^  t 
COM  phOO) 


Tt  oi-iioin 
r^  00  in  ^  in 
oj  r^  "<t  oj  N 

1-1  CO  1-1  in  o 

0>  00  00  t^  t»» 


CO"*  CO  CO  1-1 

CO  t  t*-H  CO 

COM  00  M  CM 

^  00  1-1  in  00 
CO  in  in  ■*  CO 


CO 

CO"*  M  M  CO 

CO  mo  00  o 
00  o  t^  CO  00 
o  CO ^mm 

CO  M  1-1  o  o> 
^^^_iO 


oomb>QO 

N  CO  1-1  00 

05  CO  m  1-1 
toco  r« CO 
CO  o  ^  1-1 
00  t^mco 
oooo 


"i*  i-<  05  00 

CO*  mm 

I^CO*-  CO 

r^omco 

^  M  CO  't 

00  t^m  CO 
oooo 


H 


MOCO^  ^ 
M  CO  05  11  1-1 

*•  00  1-1  *•  m 
CO  1-1  r*  M  r* 

1-11-1  O  O  05 
M  M  M  M  1-1 


m  ^  M^co 

00  n  05  O  CO 

^  CO  05  m  00 

M  t*  1-1  coo 

05  00  00  h«  t« 


M  t^  M  coco 

CO  CO  M  05  nt 
05  00  m  00  95 

*  ooMm  00 
CO  mm  *"  CO 


CO 

Mao*<  a>05 
Mm  CO  i-i  CO 
CO  00  m  CO  00 
1-1  CO  m  CO  CO 

CO  N  1-1  O  05 

^^_^o 


co-^  t^o 
com^  o 

^  CO  00  1-1 
05  t  M  ^ 

mcooor* 
00  r^mco 

oooo 


m 

N 

M 
M 


M  1-1  m  h*  o 

r«  M  CO  95  ^ 
00  CO  CO  00  o 
CO  N  N>  M  00 
1-1  ri  O  O  95 
M  N  MM  11 


^  00  M  095 
95  CO  CO  COO 
95  00  m  O  "* 

M  t^  M  r*i-i 

95  00  00  t^  t« 


00  t^  95  M  t» 

m  ooco  r«m 
m  *  1-1  m  CO 

m05  CO  CO  95 

CO  m  m  ^  CO 


95 

CO  C0 11 1*  1-1 
r^m  M  ^  CO 
eoco-^moo 

M*"  CO  I*  r* 

CO  M  iiO  95 
rHri,^.-iO 


1-1  r^o  o 
m  o  COM 

95  00  t^  95 
O  r«  95  95 
h*  ^  95  95 

00  r«m  CO 

OOOO 


M»-i  C0  95^ 
M  00  CO  t*  O 

CO  t^^  com 
r»  M  00  CO  00 

n  n  O  O  95 
MM  M  M  ix 


•-ioo5mco 

O  CO  CO  1-1  00 

mco  OC0  05 

CO  00  CO  t>.  1-1 

05  00  00  t^  r^ 


CO  mcom^ 
mo  -H  ■*  CO 

im  00  M  CO 

cooco  r»o 
cocom  •*•* 


CO 
05  O  1-1  t"«  CO 

n  m  r*co  r^ 
1-1  *•  M  ^  oo 

CO  m  t«  00  00 

CO  M  1-1  O  05 

IM  rN   l-H  H  O 


mm  05  05 

1-1  M  *co 

CO  o  1-1  n 

M  1-1  CO"* 
OOCO  i-iM 

00  r*  CO  ^ 
oooo 


^05m  o  r* 

In.  CO  O  CO  05 

r«cM  C0  00  05 

t*  CO  00  CO  00 
n  r4  O  O  95 
MNM  Mil 


00  ix  CO  00  *■ 

o  00  o  com 
o  00  CO  i-im 

*■  OO  CO  00  M 
05  00  00  t>»  t^ 


mo  ^  CO  t» 
*•  M  m  •->  CO 
r^r^Tf  05O 

CO  O  't  I"-  rl 

coco  m  t  rf 


05 

M  00^  o  t 
coco  11 00  r* 

00  M  n  CO  00 
CO  CO  00  95  95 
CO  M  1-1  O  95 
,^  ^  rH  n  O 


M  C0  95M 
CO  11  CO  O 
m  O  1  1 
CO  •*  M  (^ 
95  t»  CO  *• 

oot*co  ■* 

OOOO 


«0 

05 


CON,  00  050 
K  K  N  KOO 
0)  05  05  05  05 


•nMO^^UJ       COK00050 

00  00  00  00  00        OOOOOOOOO) 
O50505O5O5       050595^05 


05  05  95  05  95 
05  05  05  95  05 


CO  N.  00  05 
05  05  05  05 
95  05  05  05 


(29) 


Table  II.     Values  of  1— r^ 


.  000        1  .  000  000  000  000  000  000  000  000  000  999  999 

.001           .999  999  999  999  998  998  998  997  997  997  996 

.002  996  996  995  995  994  994  993  993  992  992 

.003  991  990  990  989  988  988  987  986  986  985 

.004  984  983  982  982  981  980  979  978  977  976 

.OOS  975  974  973  972  971  970  969  968  966  965 

.006  964  963  962  960  959  958  956  955  954  952 

.007  951  950  948  947  945  944  942  941  939  938 

.008  936  934  933  931  929  928  926  924  923  921 

.009  919  917  915  914  912  910  908  906  904  902 

.010  900  898  896  894  892  890  888  886  883  881 

Oil  879  877  875  872  870  868  865  863  861  858 

.012  856  854  851  849  846  844  841  839  836  834 

.013  831  828  826  823  820  818  815  812  810  807 

.014  804  801  798  796  793  790  787  784  781  778 

OlS  775  772  769  766  763  760  757  754  750  747 

.016  744  741  738  734  731  728  724  721  718  714 

.017  711  708  704  701  697  694  690  687  683  680 

.018  676  672  669  665  661  658  654  650  647  643 

.019  639  635  631  628  624  620  616  612  608  604 

.020  600  596  592  588  584  580  576  572  567  563 

.021  559  555  551  546  542  538  533  529  525  520 

.022  516  512  507  503  498  494  489  485  480  476 

.023  All  466  462  457  452  448  443  438  434  429 

.024  424  419  414  410  405  400  395  390  385  380 

.025  375  370  365  360  355  350  345  340  334  329 

.026  324  319  314  308  303  298  292  287  282  276 

.027  271  266  260  255  249  244  238  233  227  222 

.028  216  210  205  199  193  188  182  176  171  165 

.029  159  153  147  142  136  130  124  118  112  106 

.030  100  094  088  082  076  070  064  058  051  045 

.031  039  033  027  020  014  008  001  995  989  982 

.032           .998  976  970  963  957  950  944  937  931  924  918 

.033  911  904  898  891  884  878  871  864  858  851 

.034  844  837  830  824  817  810  803  796  789  782 

.035  775  768  761  754  747  740  733  726  718  711 

.036  704  697  690  682  675  668  660  653  646  638 

.037  631  624  616  609  601  594  586  579  571  564 

.038  556  548  541  533  525  518  510  502  495  487 

.039  479  471  463  456  448  440  432  424  416  408 

.040  400  392  384  376  368  360  352  344  335  327 

.041  319  311  303  294  286  278  269  261  253  244 

.042  236  228  219  211  202  194  185  177  168  160 

.043  151  142  134  125  116  108  099  090  082  073 

.044  064  055  046  038  029  020  Oil  002  993  984 

.045           .997  975  966  957  948  939  930  921  912  902  893 

.046  884  875  866  856  847  838  828  819  810  800 

.047  791  782  772  763  753  744  734  725  715  706 

.048  696  686  677  667  657  648  638  628  619  609 

.049  599  589  579  570  560  550  540  530  520  510 

.050  500  490  480  470  460  450  440  430  419  409 

(30) 


r 


Table  II.     Values  of  1— r^ 

0  123456789 


.OSO  .997  500  490  480  470  460  450  440  430  419  409 

,051  399  389  379  368  358  348  337  327  317  306 

,052  296  286  275  265  254  244  233  223  212  202 

.053  191  180  170  159  148  138  127  116  106  095 

.054  084  073  062  052  041  030  019  008  997  986 

.055  .996  975  964  953  942  931  920  909  898  886  875 

.056  864  853  842  830  819  808  796  785  774  762 

.057  751  740  728  717  705  694  682  671  659  648 

,058  636  624  613  601  589  578  566  554  543  531 

.059  519  507  495  484  472  460  448  436  424  412 

.060  400  388  376  364  352  340  328  316  303  291 

.061  279  267  255  242  230  218  205  193  181  168 

.062  156  144  131  119  1.06  094  081  069  056  044 

.063  031  018  006  993  980  968  955  942  930  917 

.064  .995  904  891  878  866  853  840  827  814  801  788 

.065  775  762  749  736  723  710  697  684  670  657 

.066  644  631  618  604  59^1  578  564  551  538  524 

.067  511  498  484  471  457  444  430  417  403  390 

.068  376  362  349  335  321  308  294  280  267  253 

.069  239  225  211  198  184  170  156  142  128  114 

.070  100  086  072  058  044  030  016  002  987  973 

.071  .994  959  945  931  916  902  888  873  859  845  830 

.072  816  802  787  773  758  744  729  715  700  686 

.073  671  656  642  627  612  598  583  568  554  539 

.074  524  509  494  480  465  450  435  420  405  390 

.075  375  360  345  330  315  300  285  270  254  239 

.076  224  209  194  178  163  148  132  117  102  086 

.077  071  056  040  025  009  994  978  963  947  932 

.078  .993  916  900  885  869  853  838  822  806  791  775 

.079  759  743  727  712  696  680  664  648  632  616 

.080  600  584  568  552  536  520  504  488  471  455 

.081  439  423  407  390  374  358  341  325  309  292 

.082  276  260  243  227  210  194  177  161  144  128 

.083  111  094  078  061  044  028  Oil  994  978  961 

.084  .992  944  927  910  894  877  860  843  826  809  792 

.085  775  758  741  724  707  690  673  656  638  621 

.086  604  587  570  552  535  518  500  483  466  448 

.087  431  414  396  379  361  344  326  309  291  274 

.088  256  238  221  203  185  168  150  132  115  097 

.089  079  061  043  026  008  990  972  954  936  918 

.090  .991  900  882  864  846  828  810  792  774  755  737 

.091  719  701  683  664  646  628  609  591  573  554 

.092  536  518  499  481  462  444  425  407  388  370 

.093  351  332  314  295  276  258  239  220  202  183 

.094  164  145  126  108  089  070  051  032  013  994 

.095  .990  975  956  937  918  899  880  861  842  822  803 

.096  784  765  746  726  707  688  668  649  630  610 

.097  591  572  552  533  513  494  474  455  435  416 

.098  396  376  357  337  317  298  278  258  239  219 

.099  199  179  159  MO  120  100  080  060  040  020 

.100  000  980  960  940  920  900  880  860  839  819 

(31) 


Table  II.     Values  of  1— r^ 


r  0  1234S6789 

100  .990  000  980  960  940  920  900  880  860  839  819 

.101  .989  799  779  759  738  718  698  677  657  637  616 

.102  596  576  555  535  514  494  473  453  432  412 

.103  391  370  350  329  308  288  267  246  226  205 

104  184  163  142  122  101  080  059  038  017  996 

105  .988  975  954  933  912  891  870  849  828  806  785 

.106  764  743  722  700  679  658  636  615  594  572 

107  551  530  508  487  465  444  422  401  379  358 

108  336  314  293  271  249  228  206  184  1^63  141 

109  119  097  075  054  032  010  988  966  944  922 

110  .987  900  878  856  834  812  790  768  746  723  701 

111  679  657  635  612  590  568  545  523  501  478 

112  456  434  411  389  366  344  321  299  276  254 
.113  231  208  186  163  140  118  095  072  050  027 

114  004  981  958  936  913  890  867  844  821  798 

lis  .986  775  752  729  706  683  660  637  614  590  567 

,116  544  521  498  474  451  428  404  381  358  334 

117  311  288  264  241  217  1.94  1.70  1.47  123  100 

.118  076  052  029  005  981  958  934  910  887  863 

119  .985  839  815  791  768  744  720  696  672  648  624 

.120  600  576  552  528  504  480  456  432  407  383 

.121  359  335  311  286  262  238  213  189  165  140 

.122  116  092  067  043  018  994  969  945  920  896 

.123  .984  871  846  822  797  772  748  723  698  674  649 

.124  624  599  574  550  525  500  475  450  425  400 

12S  375  350  325  300  275  250  225  200  174  149 

.126  124  099  074  048  023  998  972  947  922  896 

.127  .983  871  846  820  795  769  744  718  693  667  642 

.128  616  590  565  539  513  488  462  436  411  385 

.129  359  333  307  282  256  230  204  178  152  126 

,130  100  074  048  022  996  970  944  918  891  865 

.131  .982  839  813  787  760  734  708  681  655  629  602 

.132  576  550  523  497  470  444  417  391  364  338 

.133  311  284  258  231  204  178  151  124  098  071 

,134  044  017  990  964  937  910  883  856  829  802 

.135  .981775  748  721  694  667  640  613  586  558  531 

,136  504  477  450  422  395  368  340  313  286  258 

.137  231  204  176  149  121  094  066  039  Oil  984 

.138  .980  956  928  901  873  845  818  790  762  735  707 

.139  679  651  623  596  568  540  512  484  456  428 

,140  400  372  344  316  288  260  232  204  175  147 

.141  119  091  063  034  006  978  949  921  893  864 

.142  .979  836  808  779  751  722  694  665  637  608  580 

.143  551  522  494  465  436  408  379  350  322  293 

.144  264  235  206  178  149  120  091  062  033  004 

.145  .978  975  946  917  888  859  830  801  772  742  713 

.146  684  655  626  596  567  538  508  479  450  420 

.147  391  362  332  303  273  244  214  185  155  126 

,148  096  066  037  007  977  948  918  888  859  829 

.149  .977  799  769  739  710  680  650  620  590  560  530 

.150  500  470  440  410  380  350  320  290  259  229 

(32) 


r 


Table  II.     Values  of  1— i^ 

0  123456789 


.ISO  .977  500  470  440  410  380  350  320  290  259  229 

.151  199  169  139  108  078  048  017  987  957  928 

.152  .976  896  866  835  805  774  744  713  683  652  622 

.153  591  560  530  499  468  438  407  376  346  315 

,154  284  253  222  192  161  130  099  068  037  006 

.155  .975  975  944  913  882  851  820  789  758  726  695 

.156  664  633  602  570  539  508  476  445  414  382 

.157  351  320  288  257  225  194  162  131  099  068 

.158  036  004  973  941  909  878  846  814  783  751 

.159  .974  719  687  655  624  592  560  528  496  454  432 

.160  400  368  336  304  272  240  208  176  143  111 

.161  079  047  015  982  950  918  885  853  821  788 

.162  .973  756  724  691  659  626  594  561  529  496  464 

.163  431  398  366  333  300  268  235  202  170  137 

.164  104  071  038  006  973  940  907  874  841  808 

.165  .972  775  742  709  676  643  610  577  544  510  477 

.166  444  411  378  344  311  278  244  211  178  144 

.167  111  078  044  Oil  977  944  910  877  843  810 

.168  .971776  742  709  675  641  608  574  540  507  473 

.169  439  405  371  338  304  270  236  202  168  134 

.170  100  066  032  998  964  930  896  862  827  793 

.171  .970  759  725  691  656  622  588  553  519  485  450 

.172  416  382  347  313  278  244  209  175  140  106 

.173  071  036  002  967  932  898  863  828  794  759 

.174  .969  724  689  654  620  585  550  515  480  445  410 

.175  375  340  305  270  235  200  165  130  094  059 

.176  024  989  954  918  883  848  812  777  742  706 

.177  .968  671  636  600  565  529  494  458  423  387  352 

.178  316  280  245  209  173  138  102  066  031  995 

179  .967  959  923  887  852  816  780  744  708  672  636 

.180  600  564  528  492  456  420  384  348  311  275 

.181  239  203  167  130  094  058  021  985  949  912 

.182  .966  876  840  803  767  730  694  657  621  584  548 

.183  511  474  438  401  364  328  291  254  218  181 

.184  144  107  070  034  997  960  923  886  849  812 

.185  .965  775  738  701  664  627  590  553  516  478  441 

.186  404  367  330  292  255  218  180  143  106  068 

.187  031  994  956  919  881  844  806  769  731  694 

.188  .964  656  618  581  543  505  468  430  392  355  317 

.189  279  241  203  166  128  090  052  014  976  938 

.190  .963  900  862  824  786  748  710  672  634  595  557 

.191  519  481  443  404  366  328  289  251  213  174 

.192  136  098  059  021  982  944  905  867  828  790 

.193  .962  751  712  674  635  596  558  519  480  442  403 

194  364  325  286  248  209  170  131  092  053  014 

.195  .961975  936  897  858  819  780  741  702  662  623 

.196  584  545  506  466  427  388  348  309  270  230 

.197  191  152  112  073  033  994  954  915  875  836 

.198  .960  796  756  717  677  637  598  558  518  479  439 

.199  399  359  319  280  240  200  160  120  030  040 

.200  000  960  920  880  840  800  760  720  679  639 

(33) 


Table  II.  Values  of  1— r^ 

r  0  1234S6789 

.200  .960  000  960  920  880  840  800  760  720  679  639 

.201  .959  599  559  519  478  438  398  357  317  277  236 

.202  196  156  115  075  034  994  953  913  872  832 

.203  .958  791  750  710  669  628  588  547  506  466  425 

.204  384  343  302  262  221  180  139  098  057  016 

.20S  .957  975  934  893  852  811  770  729  688  646  605 

.206  564  523  482  440  399  358  316  275  234  192 

.207  151  110  068  027  985  944  902  861  819  778 

.208  .956  736  694  653  611  569  528  486  444  403  361 

.209  319  277  235  194  152  110  068  026  984  942 

.210  .955  900  858  816  774  732  690  648  606  563  521 

.211  479  437  395  352  310  268  225  183  141  098 

.212  056  014  971  929  886  844  801  759  716  674 

.213  .954  631  588  546  503  460  418  375  332  290  247 

.214  204  161  118  076  033  990  947  904  861  818 

.215  .953  775  732  689  646  603  560  517  474  430  387 

.216  344  301  258  214  171  128  084  041  998  954 

.217  .952  911  868  824  781  737  694  650  607  563  520 

.218  476  432  389  345  301  258  214  170  127  083 

.219  039  995  951  908  864  820  776  732  688  644 

.220  .951  600  556  512  468  424  380  336  292  247  203 

.221  159  115  071  026  982  938  893  849  805  760 

.222  .950  716  672  627  583  538  494  449  405  360  316 

.223  271  226  182  137  092  048  003  958  914  869 

.224  .949  824  779  734  690  645  600  555  510  465  420 

.225  375  330  285  240  195  150  105  060  014  969 

.226  .948  924  879  834  788  743  698  652 

.227  471  426  380  335  289  244  198 

.228  016  970  925  879  833  788  742 

.229  .947  559  513  467  422  376  330  284 

.230  100  054  008  962  916  870  824 

.231  .946  639  593  547  500  454  408  361 

.232  176  130  083  037  990  944  897 

.233  .945  711  664  618  571  524  478  431 

.234  244  197  150  104  057  010  963 

.235  .944  775  728  681  634  587  540  493  446  398  351 

.236  304  257  210  162  115  068  020  973  926  878 

.237  .943  831  784  736  689  641  594  546  499  451  404 

.238  356  308  261  213  165  118  070  022  975  927 

.239  .942  879  831  783  736  688  640  592  544  496  448 

.240  400  352  304  256  208  160  112  064  015  967 

.241  .941  919  871  823  774  726  678  629  581  533  484 

.242  436  388  339  291  242  194  145  097  048  000 

.243  .940  951  902  854  805  756  708  659  610  562  513 

.244  464  415  36S  318  269  220  171  122  073  024 

.245  .939  975  926  877  828  779  730  681  632  582  533 

.246  484  435  386  336  287  238  188  139  090  040 

.247  .938  991  942  892  843  793  744  694  645  595  546 

.248  496  446  397  347  297  248  198  148  099  049 

.249  .937  999  949  899  850  800  750  700  650  600  550 

.250  500  450  400  350  300  250  200  150  099  049 

(34) 


607 

562 

516 

153 

107 

062 

696 

651 

605 

238 

192 

146 

778 

731 

685 

315 

269 

222 

851 

804 

758 

384 

338 

291 

916 

869 

822 

Table  II.  Values  of  1— r* 

r  0               1234S6789 

.250  .937  500  450  400  350  300  250  200  150  099  049 

.251  .936  999  949  899  848  798  748  697  647  597  546 

.252  496  446  395  345  294  244  193  143  092  042 

.253  .935  991  940  890  839  788  738  687  636  586  535 

.254  484  433  382  332  281  230  179  128  077  026 

.255  .934  975  924  873  822  771  720  669  618  566  515 

.256  464  413  362  310  259  208  156  105  054  002 

.257  .933  951  900  848  797  745  694  642  591  539  488 

.258  436  384  333  281  229  178  126  074  023  971 

.259  .932  919  867  815  764  712  660  608  556  504  452 

.260  400  348  296  244  192  140  088  036  983  931 

.261  .931  789  827  775  722  670  618  565  513  461  408 

.262  356  304  251  199  146  094  041  989  936  884 

.263  .930  831  778  726  673  620  568  515  462  410  357 

.264  304  251  198  146  093  040  987  934  881  828 

.265  .929  775  722  669  616  563  510  457  404  350  297 

.266  244  191  138  084  031  978  924  871  818  764 

.267  .928  711  658  604  551  497  444  390  337  283  230 

.268  176  122  069  015  961  908  854  800  747  693 

.269  .927  639  585  531  478  424  370  316  262  208  154 

.270  100  046  992  938  884  830  776  722  667  613 

.271  .926  559  505  451  396  342  288  233  1.79  125  070 

.272  016  962  907  853  798  744  689  635  580  526 

.273  .925  471  416  362  307  252  198  143  088  034  979 

.274  .924  924  869  814  760  705  650  595  540  485  430 

,275  375  320  265  210  155  100  045  990  934  879 

.276  .923  824  769  714  658  603  548  492  437  382  326 

.277  271  216  160  105  049  994  938  883  827  772 

.278  .922  716  660  605  549  493  438  382  326  271  215 

.279  159  103  047  992  936  880  824  768  712  656 

.280  .921600  544  488  432  376  320  264  208  151  095 

.281  039  983  927  870  814  758  701  645  589  532 

.282  .920  476  420  363  307  250  194  137  081  024  968 

.283  .919  911  854  798  741  684  628  571  514  458  401 

.284  344  287  230  174  117  060  003  946  889  832 

.285  .918  775  718  661  604  547  490  433  376  318  261 

.286  204  147  090  032  975  918  860  803  746  688 

.287  .917  631  574  516  459  401  344  286  229  1.71  114 

.288  056  998  941  883  825  768  710  652  595  537 

.289  .916  479  421  363  306  248  190  132  074  016  958 

.290  .915  900  842  784  726  668  610  552  494  435  377 

.291  319  261  203  144  086  028  969  911  853  794 

.292  .914  736  678  619  561  502  444  385  327  268  210 

.293  151  092  034  975  916  858  799  740  682  623 

.294  .913  564  505  446  388  329  270  211  152  093  034 

.295  .912  975  916  857  798  739  680  621  562  502  443 

.296  384  325  266  206  147  088  028  969  910  850 

.297  .911  791  732  672  613  553  494  434  375  315  256 

.298  196  136  077  017  957  898  838  778  719  659 

.299  .910  599  539  479  420  360  300  240  1_80  120  060 

.300  000  940  880  820  760  700  640  580  519  459 

(36) 


Table  II.  Values  of  1— r^ 

r  0  123456789 

.300  .910  000  940  880  820  760  700  640  580  519  459 

.301  .909  399  339  279  218  158  098  037  977  917  856 

.302  .908  796  736  675  615  554  494  433  373  312  252 

.303  191  130  070  009  948  888  827  766  706  645 

.304  .907  584  523  462  402  341  280  219  158  097  036 

.305  .906  975  914  853  792  731  670  609  548  486  425 

.306  364  303  242  180  119  058  996  935  874  812 

.307  .905  751  690  628  567  505  444  382  321  259  198 

.308  136  074  013  951  889  828  766  704  643  581 

.309  .904  519  457  395  334  272  210  148  086  024  962 

.310  .903  900  838  776  714  652  590  528  466  403  341 

.311  279  217  155  092  030  968  905  843  781  718 

.312  .902  656  594  531  469  406  344  281  219  156  094 

.313  031  968  906  843  780  718  655  592  530  467 

.314  .901  404  341  278  216  153  090  027  964  901  838 

.31S  .900  775  712  649  586  523  460  397  334  270  207 

.316  144  081  018  954  891  828  764  701  638  574 

.317  .899  511  448  384  321  257  194  130  067  003  940 

.318  .898  876  812  749  685  621  558  494  430  367  303 

.319  239  175  111  048  984  920  856  792  728  664 

.320  .897  600  536  472  408  344  280  216  152  087  023 

.321  .896  959  895  831  766  702  638  573  509  445  380 

.322  316  252  187  123  058  994  929  865  800  736 

.323  .895  671  606  542  477  412  348  283  218  154  089 

.324  024  959  894  830  765  700  635  570  505  440 

.32S  .894  375  310  245  180  115  050  985  920  854  789 

.326  .893  724  659  594  528  463  398  332  267  202  136 

.327  071  006  940  875  809  744  678  613  547  482 

.328  .892  416  350  285  219  153  088  022  956  891  825 

.329  .891  759  693  627  562  496  430  364  298  232  166 

.330  100  034  968  902  836  770  704  638  571  505 

.331  .890  439  373  307  240  174  108  041  975  909  842 

.332  ,889  776  710  643  577  510  444  377  311  244  178 

.333  111  044  978  911  844  778  711  644  578  511 

.334  .888  444  377  310  244  177  110  043  976  909  842 

.335  .887  775  708  641  574  507  440  373  306  238  171 

.336  104  037  970  902  835  768  700  633  566  498 

.337  .886  431  364  296  229  161  094  026  959  891  824 

.338  .885  756  688  621  553  485  418  350  282  215  147 

.339  079  Oil  943  876  808  740  672  604  536  468 

.340  .884  400  332  264  196  128  060  992  924  855  787 

.341  .883  719  651  583  514  446  378  309  241  173  104 

.342  036  968  899  831  762  694  625  557  488  420 

.343  .882  351  282  214  145  076  008  939  870  802  733 

.344  .881  664  595  526  458  389  320  251  182  113  044 

.345  .880  975  906  837  768  699  630  561  492  422  353 

.346  284  215  146  076  007  938  868  799  730  660 

.347  .879  591  522  452  383  313  244  174  105  035  966 

.348  .878  896  826  757  687  617  548  478  408  339  269 

.349  199  129  059  990  920  850  780  710  640  570 

.350  .877  500  430  360  290  220  150  080  010  939  869 

(36) 


Table  II.  Values  of  1— r^ 

r  0               123456789 

.330  .877  500  430  360  290  220  150  080  010  939  869 

.351  .876  799  729  659  588  518  448  377  307  237  166 

.352  096  026  955  885  814  744  673  603  532  462 

.353  .875  391  320  250  179  108  038  967  896  826  755 

.354  .874  684  613  542  472  401  330  259  188  117  046 

.355  .873  975  904  833  762  691  620  549  478  406  335 

.356  264  193  122  050  979  908  836  765  694  622 

.357  .872  551  480  408  337  265  194  122  051  979  908 

.358  .871  836  764  693  621  549  478  406  334  263  191 

.359  119  047  975  904  832  760  688  616  544  472 

.360  .870  400  328  256  184  112  040  968  896  823  751 

.361  .869  679  607  535  462  390  318  245  173  101  028 

.362  .868  956  884  811  739  666  594  521  449  376  304 

.363  231  158  086  013  940  868  795  722  650  577 

.364  .867  504  431  358  286  213  140  067  994  921  848 

.365  .866  775  702  629  556  483  410  337  264  190  117 

.366  044  971  898  824  751  678  604  531  458  384 

.367  .865  311  238  164  091  017  944  870  797  723  650 

.368  ,864  576  502  429  355  281  208  134  060  987  913 

.369  .863  839  765  691  618  544  470  396  322  248  174 

.370  100  026  952  878  804  730  656  582  507  433 

.371  .862  359  285  211  136  062  988  913  839  765  690 

.372  .861  616  542  467  393  318  244  169  095  020  946 

.375  .860  871  796  722  647  572  498  423  348  274  199 

.374  124  049  974  900  825  750  675  600  525  450 

.375  .859  375  300  225  150  075  000  925  850  774  699 

.376  .858  624  549  474  398  323  248  172  097  022  946 

.377  .857  871  796  720  645  569  494  418  343  267  192 

.378  116  040  965  889  813  738  662  586  511  435 

.379  .856  359  283  207  132  056  980  904  828  752  676 

.380  .855  600  524  448  372  296  220  144  068  991  915 

.381  .854  839  763  687  610  534  458  381  305  229  152 

.382  076  000  923  847  770  694  617  541  464  388 

.383  .853  311  234  158  081  004  928  851  774  698  621 

.384  .852  544  467  390  314  237  160  083  006  929  852 

.385  .851  775  698  621  544  467  390  313  236  158  081 

.386  004  927  850  772  695  618  540  463  386  308 

.387  .850  231  154  076  999  921  844  766  689  611  534 

.388  .849  456  378  301  223  145  068  990  912  835  757 

.389  .848  679  601  523  446  368  290  212  134  056  978 

.390  .847  900  822  744  666  588  510  432  354  275  197 

.391  119  041  963  884  806  728  649  571  493  414 

.392  .846  336  258  179  101  022  944  865  787  708  630 

.393  .845  551  472  394  315  236  158  079  000  922  843 

.394  .844  764  685  606  528  449  370  291  212  133  054 

.395  .843  975  896  817  738  659  580  501  422  342  263 

.396  184  105  025  946  867  788  708  629  550  470 

.397  .842  391  312  232  153  073  994  914  835  755  676 

.398  .841  596  516  437  357  277  198  118  038  959  879 

.399  .840  799  719  639  560  480  400  320  240  160  080 

.400  000  920  840  760  680  600  520  440  359  279 

(87) 


Table  II.  Values  of  1— r* 

r  0  1234S6789 

.400  .840  000  920  840  760  680   600  520  440  359  279 

.401  .839  199  119  039  958  878  798  717  637  557  476 

.402  .838  396  316  235  155  074  994  913  833  752  672 

.403  .837  591  510  430  349  268  188  107  026  946  865 

.404  .836  784  703  622  542  461  380  299  218  137  056 

.405  .835  975  894  813  732  651  570  489  408  326  245 

.406  164  083  002  920  839  758  676  595  514  432 

.407  .834  351  270  188  107  025  944  862  781  699  618 

.408  .833  536  454  373  291  209  128  046  964  883  801 

.409  .832  719  637  555  474  392  310  228  146  064  982 

.410  .831  900  818  736  654  572  490  408  326  243  161 

.411  079  997  915  832  750  668  585  503  421  338 

.412  .830  256  174  091  009  926  844  761  679  596  514 

.413  .829  431  348  266  183  100  018  935  852  770  687 

.414  .828  604  521  438  356  273  190  107  024  941  858 

.415  .827  775  692  609  526  443  360  277  194  110  027 

.416  .826  944  861  778  694  611  528  444  361  278  194 

.417  111  028  944  861  777  694  610  527  443  360 

.418  .825  276  192  109  025  941  858  774  690  607  523 

.419  .824  439  355  271  188  104  020  936  852  768  684 

.420^  .823  600  516  432  348  264  180  096  012  927  843 

.421  .822  759  675  591  506  422  338  253  169  085  000 

.422  .821  916  832  747  663  578  494  409  325  240  156 

.423  071  986  902  817  732  648  563  478  394  309 

.424  .820  224  139  054  970  885  800  715  630  545  460 

.425  .819  375  290  205  120  035  950  865  780  694  609 

.426  .818  524  439  354  268  183  098  012  927  842  756 

.427  .817  671  586  500  415  329  244  158  073  987  902 

.428  .816  816  730  645  559  473  388  302  216  131  045 

.429  .815  959  873  787  702  616  530  444  358  272  186 

.430  100  014  928  842  756  670  584  498  411  325 

.431  .814  239  153  067  980  894  808  721  635  549  462 

.432  .813  376  290  203  117  030  944  857  771  684  598 

.433  .812  511  424  338  251  164  078  991  904  818  731 

.434  .811  644  557  470  384  297  210  123  036  949  862 

.435  .810  775  688  601  514  427  340  253  166  078  991 

.436  .809  904  817  730  642  555  468  380  293  206  ^18 

.437  031  944  856  769  681  194  506  419  331  244 

.438  .808  156  068  981  893  805  718  630  542  455  367 

.439  .807  279  191  103  016  928  840  752  664  576  488 

.440  .806  400  312  224  136  048  960  872  784  695  607 

.441  .805  519  431  343  254  166  078  989  901  813  724 

.442  .804  636  548  459  371  282  194  105  017  928  840 

.443  .803  751  662  574  485  396  308  219  130  042  953 

.444  .802  864  775  686  598  509  420  331  242  153  064 

.445  .801  975  886  797  708  619  530  441  352  262  173 

.446  084  995  906  816  727  638  548  459  370  280 

.447  .800  191  102  012  923  833  744  654  565  475  386 

.448  .799  296  206  117  027  937  848  758  668  579  489 

.449  .798  399  309  219  130  040  950  860  770  680  590 

.450  .797  500  410  320  230  140  050  960  870  779  689 

(38) 


Table  II.  Values  of  1— r^ 

r  0  1234S6789 

.450  .797  500  410  320  230  140  050  960  870  779  689 

.451  .796  599  509  419  328  238  148  057  967  877  786 

.452  .795  696  606  515  425  334  244  153  063  972  882 

.453  .794  791  700  610  519  428  338  247  156  066  975 

.454  .793  884  793  702  612  521  430  339  248  157  066 

.455  .792  975  884  793  702  611  520  429  338  246  155 

.456  064  973  882  790  699  608  516  425  334  242 

.457  .791  151  060  968  877  785  694  602  511  419  328 

.458  .790  236  144  053  961  869  778  686  594  503  411 

.459  .789  319  227  135  044  952  860  768  676  584  492 

.460  .788  400  308  216  124  032  940  848  756  663  571 

.461  .787  479  387  295  202  110  018  925  833  741  648 

.462  .786  556  464  371  279  186  094  001  909  816  724 

.463  .785  631  538  446  353  260  168  075  982  890  797 

.464  .784  704  611  518  426  333  240  147  054  961  868 

.465  .783  775  682  589  496  403  310  217  124  030  937 

.466  .782  844  751  658  564  471  378  284  191  098  004 

.467  .781  911  818  724  631  537  444  350  257  163  070 

.468  .780  976  882  789  695  601  508  414  320  227  133 

.469  039  945  851  758  664  570  476  382  288  T94 

.470  .779  100  006  912  818  724  630  536  442  347  253 

.471  .778  159  065  971  l76  782  688  593  499  405  310 

.472  .777  216  122  027  933  838  744  649  555  460  366 

.473  .776  271  176  082  987  892  798  703  608  514  419 

.474  .775  324  229  134  040  945  850  755  660  565  470 

.475  .774  375  280  185  090  995  900  805  710  614  519 

.476  .773  424  329  234  138  043  948  852  757  662  566 

.477  .772  471  376  280  185  089  994  898  803  707  612 

.478  .771  516  420  325  229  133  038  942  846  751  655 

.479  .770  559  463  367  272  176  080  984  888  792  696 

.480  .769  600  504  408  312  216  120  024  928  831  735 

.481  .768  639  543  447  350  254  158  061  965  869  772 

.482  .767  676  580  483  387  290  194  097  001  904  808 

.483  .766  711  614  518  421  324  228  131  034  938  841 

.484  .765  744  647  550  454  357  260  163  066  969  872 

.485  .764  775  678  581  484  387  290  193  096  998  901 

.486  .763  804  707  610  512  415  318  220  123  026  928 

.487  .762  831  734  636  539  441  344  246  149  051  954 

.488  .761  856  758  661  563  465  368  270  172  075  977 

.489  .760  879  781  683  586  488  390  292  194  096  998 

.490  .759  900  802  704  606  508  410  312  214  115  017 

.491  .758  919  821  723  624  526  428  329  231  133  034 

.492  .757  936  838  739  641  542  444  345  247  148  050 

.493  .756  951  852  754  655  556  458  359  260  162  063 

.494  .755  964  865  766  668  569  470  371  272  173  074 

.495  .754  975  876  777  678  579  480  381  282  182  083 

.496  .753  984  885  786  686  587  488  388  289  190  090 

.497  .752  991  892  792  693  593  494  394  295  195  096 

.498  .751  996  896  797  697  597  498  398  298  199  099 

.499  .750  999  899  799  700  600  500  400  300  200  100 

.500  000  900  800  700  600  500  400  300  199  099 

(39) 


.748  498 

397 

297 

197 

096 

.  747  494 

393 

293 

192 

092 

.  746  488 

387 

286 

186 

085 

.745  480 

379 

278 

177 

076 

.744  470 

369 

268 

166 

065 

Table  II.     Values  of  1— r^ 

r       0  12          3  4                5  6  7  8  9 

.500  .750  000  900  800  700  600  .749  500  400  300  199  099 

.501  .748  999  899  799  698  598 

.502  .747  996  896  795  695  594 

.503  .746  991  890  790  689  588 

.504  .745  984  883  782  682  581 

.505  .744  975  874  773  672  571 

.506  .743  964  863  762  660  559  .743  458  356  255  154  052 

.507  .742  951  850  748  647  545  .742  444  342  241  139  038 

.508  .741936  834  733  631  529  .741428  326  224  123  021 

.509  .740  919  817  715  614  512  .740  410  308  206  104  002 

.510  .739  900  798  696  594  492  .739  390  288  186  083  981 

.511  .738  879  777  675  572  470  .738  368  265  163  061  958 

.512  .737  856  754  651  549  446  .737  344  241  139  036  934 

.513  .736  831  728  626  523  420  .736  318  215  112  010  907 

.514  .735  804  701  598  496  393  .735  290  187  084  981  878 

.515  .734  775  672  569  466  363  .734  260  157  054  950  847 

.516  .733  744  641  538  434  331  .733  228  124  021  918  814 

.517  .732  711  608  504  401  297  .732  194  090  987  883  780 

.518  .731676  572  469  365  261  .731158  054  950  847  743 

.519  .730  639  535  431  328  224  .730  120  016  912  808  704 

.520  .729  600  496  392  288  184  .729  080  976  872  767  663 

.521  .728  559  455  351  246  142  .728  038  933  829  725  620 

.522  .727  516  412  307  203  098  .726  994  889  785  680  576 

.523  .726  471  366  262  157  052  .725  948  843  738  634  529 

.524  .725  424  319  214  110  005  .724  900  795  690  585  480 

.525  .724  375  270  165  060  955  .723850  745  640  534  429 

.526  .723  324  219  114  008  903  .722  798  692  587  482  376 

.527  .722  271  166  060  955  849  .721744  638  533  427  322 

.528  .721216  110  005  899  793  .720  688  582  476  371  265 

.529  .720  159  053  947  842  736  .719  630  524  418  312  206 

.530  .719  100  994  888  782  676  .718  570  464  358  251  145 

.531  .718039  933  827  720  614  .717  508  401  295  189  082 

.532  .716  976  870  763  657  550  .716  444  337  231  124  018 

.533  .715  911  804  698  591  484  .715  378  271  164  058  951 

.534  .714  844  737  630  524  417  .714  310  203  096  989  882 

.535  .713  775  668  561  454  347  .713  240  133  026  918  811 

.536  .712  704  597  490  382  275  .712  168  060  953  846  738 

.537  .711631  524  416  309  201  .711094  986  879  771  664 

,538  .710  556  448  341  233  125  .710  018  910  802  695  587 

,539  .709  479  371  263  156  048  .708  940  832  724  616  508 

,540  .708  400  292  184  076  968  .707  860  752  644  535  427 

,541  .707  319  211  103  994  886  .706  778  669  561  453  344 

,542  .706  236  128  019  911  802  .705  694  585  477  368  260 

,543  .705  151  042  934  825  716  .704608  499  390  282  173 

,544  .704  064  955  846  738  629  .703  520  411  302  193  084 

,545  .702  975  866  757  648  539  .702  430  321  212  102  993 

,546  .701  884  775  666  556  447  .701  338  228  119  010  900 

,547  .700  791  682  572  463  353  .700  244  134  025  915  806 

,548  .699  696  586  477  367  257  .699  148  038  928  819  709 

,549  .698  599  489  379  270  160  .698  050  940  830  720  610 

,550  .697  500  390  280  170  060  .696  950  840  730  619  509 

(46) 


Table  II.     Values  of  1— r^ 

r       0             12          3          4                S  6  7          8          9 

.550      .697  500   390   280   170   060   .696  950  840  730  619  509 

.695  848  737  627  517  406 

.694  744  633  523  412  302 

.693  638  527  416  306  195 

.692  530  419  308  197  086 

.691420  309  198  086  975 

.690  308  196  085  974  862 

.689  194  082  971  859  748 

.688  078  966  854  743  631 

.686  960  848  736  624  512 

.685  840  728  616  503  391 

.684  718  605  493  381  268 

.683  594  481  369  256  144 

.682  468  355  242  130  017 

.681  340  227  114  001  888 

.680  210  097  984  870  757 

.679  078  964  851  738  624 

.677  944  830  717  603  490 

.676  808  694  580  467  353 

.675  670  556  442  328  214 

.674  530  416  302  187  073 

.673  388  273  159  045  930 

.672  244  129  015  900  786 

.671  098  983  868  754  639 

.669  950  835  720  605  490 

.668  800  685  570  454  339 

.667  648  532  417  302  186 

.666  494  378  263  147  032 

.665  338  222  106  991  875 

.664  180  064  948  832  716 

.663  020  904  788  671  555 

.661  858  741  625  509  392 

.660  694  577  461  344  228 

.659  528  411  294  178  061 

.658  360  243  126  009  892 

.657  190  073  956  838  721 

.656  018  900  783  666  548 

.654  844  726  609  491  374 

.653  668  550  432  315  197 

.652  490  372  254  136  018 

.651  310  192  074  955  837 

.650  128  009  891  773  654 

.648  944  825  707  588  470 

.647  758  639  520  402  283 

.646  570  451  332  213  094 

.645  380  261  142  022  903 

.644  188  068  949  830  710 

.642  994  874  755  635  5^ 

.641  798  678  558  439  ' 

.640  600  480  360  240 

.639  400  280  160  0' 

(41) 


.551 

.696  399 

289 

179 

068 

958 

.552 

.695  296 

186 

075 

965 

854 

.553 

.694  191 

080 

970 

859 

748 

,554 

.  693  084 

973 

862 

752 

641 

.555 

.691  975 

864 

753 

642 

531 

.556 

.690  864 

753 

642 

530 

419 

.557 

.689  751 

640 

528 

417 

305 

.558 

.688  636 

524 

413 

301 

189 

.559 

.687  519 

407 

295 

184 

072 

.560 

.686  400 

288 

176 

064 

952 

561 

.  685  279 

167 

055 

942 

830 

562 

.684  156 

044 

931 

819 

706 

563 

.683  031 

918 

806 

693 

580 

564 

.681  904 

791 

678 

566 

453 

565 

.680  775 

662 

549 

436 

323 

566 

.679  644 

531 

418 

304 

191 

567 

.678  511 

398 

284 

171 

057 

568 

.677  376 

262 

149 

035 

921 

569 

.676  239 

125 

Oil 

898 

784 

570 

.675  100 

986 

872 

758 

644 

571 

.673  959 

845 

731 

616 

502 

572 

.672  816 

702 

587 

473 

358 

573 

.671  671 

556 

442 

327 

212 

574 

.670  524 

409 

294 

180 

065 

575 

.669  375 

260 

145 

030 

915 

576 

.668  224 

109 

994 

878 

763 

577 

.667  071 

956 

840 

725 

609 

578 

.665  916 

800 

685 

569 

453 

579 

.664  759 

643 

527 

412 

296 

580 

.663  600 

484 

368 

252 

136 

581 

.662  439 

323 

207 

090 

974 

582 

.661  276 

160 

043 

927 

810 

583 

.660  111 

994 

878 

761 

644 

584 

.658  944 

828 

711 

594 

477 

585 

.657  775 

658 

541 

424 

307 

586 

.656  604 

487 

370 

252 

135 

587 

.655  431 

314 

196 

079 

961 

588 

.  654  256 

138 

021 

903 

785 

589 

.653  079 

961 

843 

726 

608 

590 

.651  900 

782 

664 

546 

428 

591 

.650  719 

601 

483 

364 

246 

592 

.649  536 

418 

299 

181 

062 

593 

.648  351 

232 

114 

995 

876 

594 

.647  164 

045 

926 

808 

689 

595 

.645  975 

856 

737 

618 

499 

596 

.644  784 

665 

546 

426 

307 

597 

.643  591 

472 

352 

233 

113 

598 

.642  396 

276 

157 

037 

917 

599 

.641  199 

079 

959 

840 

720 

600 

.640  000 

880 

760 

640 

520 

Table  II.     Values  of  1— r^ 


r       0  12  3  4  5  6  7  8  9 

.600  .640  000  880  760  640  520  .639  400  280  160  039  919 

.601  .638  799  679  559  438  318  .638  198  077  957  837  716 

.602  .637  596  476  355  235  114  .636  994  873  753  632  512 

,603  .636  391  270  150  029  908  .635  788  667  546  426  305 

.604  .635  184  063  942  822  701  .634  580  459  338  217  096 

.60S  .633  975  854  733  612  491  .633  370  249  128  006  885 

.606  .632  764  643  522  400  279  .632  158  036  915  794  672 

.607  .631551  430  308  187  065  .630  944  822  701  579  458 

.608  .630  336  214  093  971  849  .629  728  606  484  363  241 

.609  .629  119  997  875  754  632  .628  510  388  266  144  022 

.610  .627  900  778  656  534  412  .627  290  168  046  923  801 

.611  .626  679  557  435  312  190  .626  068  945  823  701  578 

.612  .625  456  334  211  089  966  .624  844  721  599  476  354 

.613  .624  231  108  986  863  740  .623  618  495  372  250  127 

.614  .623  004  881  758  636  513  .622  390  267  144  021  898 

.615  .621  775  652  529  406  283  .621  160  037  914  790  667 

.616  .620  544  421  298  174  051  .619  928  804  681  558  434 

.617  .619  311  188  064  941  817  .618  694  570  447  323  200 

.618  ,618  076  952  829  705  581  .617  458  334  210  087  963 

.619  .616  839  715  591  468  344  .616  220  096  972  848  724 

.620  .615  600  476  352  228  104  .614  980  856  732  607  483 

.621  .614  359  235  111  986  862  .613  738  613  489  365  240 

.622  .613  116  992  867  743  618  .612494  369  245  120  996 

.623  .611871  746  622  497  372  .611248  123  998  874  749 

.624  ,610  624  499  374  250  125  ,610  000  875  750  625  500 

.625  .609  375  250  125  000  875  .608  750  625  500  374  249 

.626  .608  124  999  874  748  623  .607  498  372  247  122  996 

.627  .606  871  746  620  495  369  .606  244  118  993  867  742 

.628  .605  616  490  365  239  113  .604  988  862  736  611  485 

.629  .604  359  233  107  982  856  .603  730  604  478  352  226 

.630  .603  100  974  848  722  596  .602  470  344  218  091  965 

.631  .601  839  713  587  460  334  .601  208  081  955  829  702 

.632  .600  576  450  323  197  070  .599  944  817  691  564  438 

.633  .599  311  184  058  931  804  .598  678  551  424  298  171 

.634  .598  044  917  790  664  537  .597  410  283  156  029  902 

.635  .596  775  648  521  394  267  .596  140  013  886  758  631 

.636  .595  504  377  250  122  995  .594  868  740  613  486  358 

.637  .594  231  104  976  849  721  .593  594  466  339  211  084 

.638  .592  956  828  701  573  445  .592  318  190  062  935  807 

.639  .591  679  551  423  296  168  .591  040  912  784  656  528 

.640  .590  400  272  144  016  888  .589  760  632  504  375  247 

.641  .589  119  991  863  734  606  .588  478  349  221  093  964 

.642  .587  836  708  579  451  322  .587  194  065  937  808  680 

.643  .586  551  422  294  165  036  .585  908  779  650  522  393 

.644  .585  264  135  006  878  749  .584  620  491  362  233  104 

.645  .583  975  846  717  588  459  .583  330  201  072  942  813 

.646  .582  684  555  426  296  167  ,582  038  908  779  650  520 

.647  .581391  262  132  003  873  .580  744  614  485  355  226 

.648  .580  096  966  837  707  577  .579  448  318  188  059  929 

.649  .578  799  669  539  410  280  .578  150  020  890  760  630 

.650  .577  500  370  240  110  980  .576  850  720  590  459  329 

(42) 


Table  II.     Values  of  1— i^ 


r       0  12  3  4                5  6          7  8  9 

.650  .577  500  370  240  110  980  .576  850  720  590  459  329 

.651  .576  199  069  939  808  678  .575  548  417  287  157  026 

.652  .574  896  766  635  505  374  .57 A  244  113  983  852  722 

.653  .573  591  460  330  199  068  .572  938  807  676  546  415 

.654  .572  284  153  022  892  761  .571630  499  368  237  106 

.655  .570975  844  713  582  451  .570  320  189  058  926  795 

.656  .569  664  533  402  270  139  .569  008  876  745  614  482 

.657  .568  351  220  088  957  825  .567  694  562  431  299  168 

.658  .567  036  904  773  641  509  .566  378  246  114  983  851 

.659  .565  719  587  455  324  192  .565  060  928  796  664  532 

.660  .564  400  268  136  004  872  .563  740  608  476  343  211 

.661  .563  079  947  815  682  550  .562  418  285  153  021  888 

.662  .561  756  624  491  359  226  .561  094  961  829  696  564 

.663  .560  431  298  166  033  900  .559  768  635  502  370  237 

.664  .559  104  971  838  706  573  .558  440  307  174  041  908 

.665  .557  775  642  509  376  243  .557  110  977  844  710  577 

.666  .556  444  311  178  044  911  .555  778  644  511  378  244 

.667  .555  111  978  844  711  577  .554444  310  177  043  910 

.668  .553  776  642  509  375  241  .553  108  974  840  707  573 

.669  .552  439  305  171  038  904  .551770  636  502  368  234 

.670  .551100  966  832  698  564  .550  430  296  162  027  893 

.671  .549  759  625  491  356  222  .549  088  953  819  685  550 

.672  .548  416  282  147  013  878  .547  744  609  475  340  206 

.673  .547  071  936  802  667  532  .546  398  263  128  994  859 

.674  .545  724  589  454  320  185  .545  050  915  780  645  510 

.675  .544  375  240  105  970  835  .543  700  565  430  294  159 

.676  .543  024  889  754  618  483  .542  348  212  077  942  806 

.677  .541671  536  400  265  129  .540  994  858  723  587  452 

.678  .540  316  180  045  909  773  .539  638  502  366  231  095 

.679  .538  959  823  687  552  416  .538  280  144  008  872  736 

.680  .537  600  464  328  192  056  .536  920  784  648  511  375 

.681  .536  239  103  967  830  694  .535  558  421  285  149  012 

.682  .534  876  740  603  467  330  .534  194  057  921  784  648 

.683  .533  511  374  238  101  964  .532  828  691  554  418  281 

.684  .532  144  007  870  734  597  .531460  323  186  049  912 

.685  .530  775  638  501  364  227  .530  090  953  816  678  541 

.686  .529  404  267  130  992  855  .528  718  580  443  306  168 

.687  .528  031  894  756  619  481  .527  344  206  069  931  794 

.688  .526  656  518  381  243  105  .525  968  830  692  555  417 

.689  .525  279  141  003  866  728  .524  590  452  314  176  038 

.690  .523  900  762  624  486  348  .523  210  072  934  795  657 

.691  .522  519  381  243  104  966  .521828  689  551  413  274 

.692  .521  136  998  859  721  582  .520  444  305  167  028  890 

.693  .519  751  612  474  335  196  .519  058  919  780  642  503 

.694  .518  364  225  086  948  809  .517  670  531  392  253  114 

.695  .516  975  836  697  558  419  .516  280  141  002  862  723 

.696  .515  584  445  306  166  027  .514  888  748  609  470  330 

.697  .514  191  052  912  773  633  .513  494  354  215  075  936 

.698  .512  796  656  517  377  237  .512  098  958  818  679  539 

.699  .511399  259  119  980  840  .510  700  560  420  280  140 

.700  .510  000  860  720  580  440  .509  300  160  020  879  739 

(«8) 


Table  II.     Values  of  1 — r^ 

r  0  12  3  4  S  6  7  8  9 

700      .510  000   860   720   580  440   .509  300   160   020   879   739 


701 

.  508  599 

459 

319 

178 

038 

.507  898 

757 

617 

477 

336 

702 

.507  196 

056 

915 

775 

634 

.506  494 

353 

213 

072 

932 

703 

.505  791 

650 

510 

369 

228 

.505  088 

947 

806 

666 

525 

704 

.504  384 

243 

102 

962 

821 

.503  680 

539 

398 

257 

116 

70S 

.502  975 

834 

693 

552 

411 

.  502  270 

129 

988 

846 

705 

706 

.501  564 

423 

282 

140 

999 

.500  858 

716 

575 

434 

292 

707 

.500  151 

010 

868 

727 

585 

.499  444 

302 

161 

019 

878 

708 

.498  736 

594 

453 

311 

169 

.498  028 

886 

744 

603 

461 

709 

.497  319 

177 

035 

894 

752 

.496  610 

468 

326 

184 

042 

710 

.495  900 

758 

616 

474 

332 

.495  190 

048 

906 

763 

621 

711 

.494  479 

337 

195 

052 

910 

.493  768 

625 

483 

341 

198 

712 

.493  056 

914 

771 

629 

486 

.492  344 

201 

059 

916 

774 

713 

.491  631 

488 

346 

203 

060 

.490  918 

775 

632 

490 

347 

714 

.490  204 

061 

918 

776 

633 

.489  490 

347 

204 

061 

918 

715 

.488  775 

632 

489 

346 

203 

.488  060 

917 

774 

630 

487 

716 

.487  344 

201 

058 

914 

771 

.486  628 

484 

341 

198 

054 

717 

.485  911 

768 

624 

481 

337 

.485  194 

050 

907 

763 

620 

718 

.484  476 

332 

189 

045 

901 

.483  758 

614 

470 

327 

183 

719 

.483  039 

895 

751 

608 

464 

.482  320 

176 

032 

888 

744 

720 

.481  600 

456 

312 

168 

024 

.480  880 

736 

592 

447 

303 

721 

.480  159 

015 

871 

726 

582 

.479  438 

293 

149 

005 

860 

722 

.478  716 

572 

427 

283 

138 

.477  994 

849 

705 

560 

416 

723 

.477  271 

126 

982 

837 

692 

.476  548 

403 

258 

114 

969 

724 

.475  824 

679 

534 

390 

245 

.475  100 

955 

810 

665 

520 

725 

.474  375 

230 

085 

940 

795 

.473  650 

505 

360 

214 

069 

726 

.472  924 

779 

634 

488 

343 

.472  198 

052 

907 

762 

616 

727 

.471  471 

326 

180 

035 

889 

.470  744 

598 

453 

307 

162 

728 

.470  016 

870 

725 

579 

433 

.469  288 

142 

996 

851 

705 

729 

.468  559 

413 

267 

122 

976 

.467  830 

684 

538 

392 

246 

730 

.467  100 

954 

808 

662 

516 

.466  370 

224 

078 

931 

785 

731 

.465  639 

493 

347 

200 

054 

.  464  908 

761 

615 

469 

222 

732 

.464  176 

030 

883 

737 

590 

.  463  444 

297 

151 

004 

853 

733 

.462  711 

564 

418 

271 

124 

.461  978 

831 

684 

538 

391 

734 

.461  244 

097 

950 

804 

657 

.460  510 

363 

216 

069 

922 

735 

.459  775 

628 

481 

334 

187 

.459  040 

893 

746 

598 

451 

736 

.458  304 

157 

010 

862 

715 

.457  568 

420 

273 

126 

978 

737 

.456  831 

684 

536 

389 

241 

.456  094 

946 

799 

651 

504 

738 

.455  356 

208 

061 

913 

765 

.454  618 

470 

322 

175 

027 

739 

.453  879 

731 

583 

436 

288 

.453  140 

992 

844 

696 

548 

740 

.452  400 

252 

104 

956 

808 

.451  660 

512 

364 

215 

067 

741 

.450  919 

771 

623 

474 

32€ 

.450  178 

029 

881 

733 

584 

742 

.449  436 

288 

139 

991 

842 

.448  694 

545 

397 

248 

100 

743 

.447  951 

802 

654 

505 

356 

.447  208 

059 

910 

762 

613 

744 

.446  464 

315 

166 

018 

869 

.445  720 

571 

422 

273 

124 

745 

.444  975 

826 

677 

528 

379 

.444  230 

081 

932 

782 

633 

746 

.  443  484 

335 

186 

036 

887 

.442  738 

588 

439 

290 

140 

747 

.441  991 

842 

692 

543 

393 

.441  244 

094 

945 

795 

646 

748 

.440  496 

346 

197 

047 

897 

.  439  748 

598 

448 

299 

149 

749 

.438  999 

849 

699 

550 

400 

.438  250 

100 

950 

800 

650 

750 

.437  500 

350 

200 

050 

900 
(44) 

.436  750 

600 

450 

299 

149 

Table  11.     Values  of  1— i^ 

r       0  12  3  4                5              6  7  8  9 

.750  .437  500  350  200  050  900  .436  750  600  450  299  149 

.751  .435  999  849  699  548  398  .435  248  097  947  797  646 

.752  .434  496  346  195  045  894  .433  744  593  443  292  142 

.753  .432  991  840  690  539  388  .432  238  087  936  786  635 

.754  .431484  333  182  032  881  .430  730  579  428  277  126 

.755  .429  975  824  673  522  371  .429  220  069  918  766  615 

.756  .428  464  313  162  010  859  .427  708  556  405  254  102 

.757  .426  951  800  648  497  345  .426  194  042  891  739  588 

.758  .425  436  284  133  981  829  .424  678  526  374  223  071 

.759  .423  919  767  615  464  312  .423  160  008  856  704  552 

.760  .422  400  248  096  944  792  .421640  488  336  183  031 

.761  .420  879  727  575  422  270  .420  118  965  813  661  508 

.762  .419  356  204  051  899  746  .418  594  441  289  136  984 

.763  .417  831  678  526  373  220  .417  068  915  762  610  457 

.764  .416  304  151  998  846  693  .415  540  387  234  081  928 

.765  .414  775  622  469  316  163  .414  010  857  704  550  397 

.766  .413  244  091  938  784  631  .412  478  324  171  018  864 

.767  .411711  558  404  251  097  .410  944  790  637  483  330 

.768  .410  176  022  869  715  561  .409  408  254  100  946  793 

.769  .408  639  485  331  178  024  .407  870  716  562  408  254 

.770  .407  100  946  792  638  484  .406  330  176  022  867  713 

.777  .405  559  405  251  096  942  .404  788  634  479  325  170 

.772  .404  016  862  707  553  398  .403  244  089  935  780  626 

.773  .402  471  316  162  007  852  .401698  543  388  234  079 

.774  .400  924  769  614  460  305  .400  150  995  840  685  530 

.775  .399  375  220  065  910  755  .398  600  445  290  134  979 

.776  .397  824  669  514  358  203  .397  048  892  737  582  426 

.777  .396  271  116  960  805  649  .395  494  338  183  027  872 

.778  .394  716  560  405  249  093  .393  938  782  626  471  315 

.779  .393  159  003  847  692  536  .392  380  224  068  912  756 

.780  .391600  444  288  132  976  .390  820  664  508  351  195 

.781  .390  039  883  727  570  414  .389  258  101  945  789  632 

.782  .388  476  320  163  007  850  .387  694  537  381  224  068 

.783  .386  911  754  598  441  284  .386  128  971  814  658  501 

.784  .385  344  187  030  874  717  .384  560  403  246  089  932 

.785  .383  775  618  461  304  147  .382  990  833  676  518  361 

.786  .382  204  047  890  732  575  .381418  260  103  946  788 

.787  .380  631  474  316  159  001  .379  844  686  529  371  214 

.788  .379  056  898  741  583  425  .378  268  110  952  795  637 

.789  .377  479  321  163  006  848  .376  690  532  374  216  058 

.790  .375  900  742  584  426  268  .375  110  952  794  635  477 

.791  .374319  161  003  844  686  .373  528  369  211  053  894 

.792  .372  736  578  419  261  102  .371944  785  627  468  310 

.793  .371151  992  834  675  516  .370  358  199  040  882  723 

.794  .369  564  405  246  087  929  .368  770  611  452  293  134 

.795  .367  975  816  657  498  339  .367  180  021  862  702  543 

.796  .366  384  225  066  907  747  .365  588  428  269  110  950 

.797  .364  791  632  472  313  153  .363  994  834  675  515  356 

.798  .363  196  036  877  717  557  .362  398  238  078  919  759 

.799  .361599  439  279  120  960  .360  800  640  480  320  160 

.800  .360  000  840  680  520  360  .359  200  040  880  719  559 

(46) 


Table  II.     Values  of  1— r^ 

r       0  12  3  4                S              6  7  8          9 

.800  .360  000  840  680  520  360  .359  200  040  880  719  559 

.801  .358  399  239  079  918  758  .357  598  437  277  117  956 

.802  .356  796  636  475  315  154  .355  994  833  673  512  352 

.803  .355  191  030  870  709  548  .354  388  227  066  906  745 

.804  .353  584  423  262  102  941  .352  780  619  458  297  136 

.80S  .351975  814  653  492  331  .351170  009  848  686  525 

.806  .350  364  203  042  880  719  .349  558  396  235  074  912 

.807  .348  751  590  428  267  105  .347  944  782  621  459  298 

.808  .347  136  974  813  651  489  .346  328  166  004  843  681 

.809  .345  519  357  195  034  872  .344  710  548  386  224  062 

.810  .343  900  738  576  414  252  .343  090  928  766  603  441 

.811  .342  279  117  955  792  630  .341468  305  143  981  818 

.812  .340  656  494  331  169  006  .339  844  681  519  356  194 

.813  .339  031  868  706  543  380  .338  218  055  892  730  567 

.814  .337  404  241  078  916  753  .336  590  427  264  101  938 

.815  .335  775  612  449  286  123  .334  960  797  634  470  307 

.816  .334  144  981  818  654  491  .333  328  164  001  838  674 

.817  .332  511  348  184  021  857  .331694  530  367  203  040 

.818  .330  876  712  549  385  221  .330  058  894  730  567  403 

.819  .329  239  075  911  748  584  .328  420  256  092  928  764 

.820  .327  600  436  272  108  944  .326  780  616  452  287  123 

.821  .325  959  795  631  466  302  .325  138  973  809  645  480 

.822  .324  316  152  987  823  658  .323  494  329  165  000  836 

.823  .322  671  506  342  177  012  .321848  683  518  354  189 

.824  .321024  859  694  530  365  .320  200  035  870  705  540 

.825  .319  375  210  045  880  715  .318  550  385  220  054  889 

.826  .317  724  559  394  228  063  .316  898  732  567  402  236 

.827  .316  071  906  740  575  409  .315  244  078  913  747  582 

.828  .314  416  250  085  919  753  .313  588  422  256  091  925 

.829  .312  759  593  427  262  096  .311930  764  598  432  266 

.830  .311100  934  768  602  436  .310  270  104  938  771  605 

.831  .309  439  273  107  940  774  .308  608  441  275  109  942 

.832  .307  776  610  443  277  110  .306  944  777  611  444  278 

.  833  .  306  1 1 1  944  778  61 1  444  .  305  278  111  944  778  61 1 

.834  .304444  277  110  944  777  .303  610  443  276  109  942 

.835  .302  775  608  441  274  107  .301940  773  606  438  271 

.836  .301104  937  770  602  435  .300  268  100  933  766  598 

.837  .299  431  264  096  929  761  .298  594  426  259  091  924 

.838  .297  756  588  421  253  085  .296  918  750  582  415  247 

.839  .296  079  911  743  576  408  .295  240  072  904  736  568 

.840  .294  400  232  064  896  728  .293  560  392  224  055  887 

.841  .292  719  551  383  214  046  .291878  709  541  373  204 

.842  .291036  868  699  531  362  .290  194  025  857  688  520 

.843  .289  351  182  014  845  676  .288  508  339  170  002  833 

.844  .287  664  495  326  158  989  .286  820  651  482  313  144 

.845  .285  975  806  637  468  299  .285  130  961  792  622  453 

.846  .284  284  115  946  776  607  .283  438  268  099  930  760 

.847  .282  591  422  252  083  913  .281744  574  405  235  066 

.848  .280  896  726  557  387  217  .280  048  878  708  539  369 

.849  .279  199  029  859  690  520  .278  350  180  010  840  670 

.850  .277  500  330  160  990  820  .276  650  480  310  139  969 

(«) 


Table  II.     Values  of  1— i^ 

r       0  12          3  4                5  6  7  8  9 

.8S0  .277  500  330  160  990  820  .276  650  480  310  139  969 

.851  .275  799  629  459  288  118  .274  948  777  607  437  266 

.8S2  .274  096  926  755  585  414  .273  244  073  903  732  562 

.853  .272  391  220  050  879  708  .271538  367  196  026  855 

.854  .270684  513  342  172  001  .269  830  659  488  317  146 

.855  .268  975  804  633  462  291  .268  120  949  778  606  435 

.856  .267  264  093  922  750  579  .266  408  236  065  894  722 

.857  .265  551  380  208  037  865  .264  694  522  351  179  008 

.858  .263  836  664  493  321  149  .262  978  806  634  463  291 

.859  .262  119  947  775  604  432  .261260  088  916  744  572 

.860  .260  400  228  056  884  712  .259  540  368  196  023  851 

.861  .258  679  507  335  162  990  .257  818  645  473  301  128 

.862  .256  956  784  611  439  266  .256  094  921  749  576  404 

.863  .255  231  058  886  713  540  .254  368  195  022  850  677 

.864  .253  504  331  158  986  813  .252  640  467  294  121  948 

.865  .251775  602  429  256  083  .250  910  737  564  390  217 

.866  .250  044  871  698  524  351  .249  178  004  831  658  484 

.867  .248  311  138  964  791  617  .247  444  270  097  923  750 

.868  .246  576  402  229  055  881  .245  708  534  360  187  013 

.869  .244  839  665  491  318  144  .243  970  796  622  448  274 

.870  .243  100  926  752  578  404  .242  230  056  882  707  533 

.871  .241359  185  Oil  836  662  .240  488  313  139  965  790 

.872  .239  616  442  267  093  918  .238  744  569  395  220  046 

.873  .237  871  696  522  347  172  .236  998  823  648  474  299 

.874  .236  124  949  774  600  425  .235  250  075  900  725  550 

.875  .234  375  200  025  850  675  .233  500  325  150  974  799 

.876  .232  624  449  274  098  923  .231748  572  397  222  046 

.877  .230  871  696  520  345  169  .229  994  818  643  467  292 

.878  .229  116  940  765  589  413  .228  238  062  886  711  535 

.879  .227  359  183  007  832  656  .226  480  304  128  952  776 

.880  .225  600  424  248  072  896  .224  720  544  368  191  015 

.881  .223  839  663  487  310  134  .222  958  781  605  429  252 

.882  .222  076  900  723  547  370  .221194  017  841  664  488 

.883  .220  311  134  958  781  604  .219  428  251  074  898  721 

.884  .218  544  367  190  014  837  .217  660  483  306  129  952 

.885  .216  775  598  421  244  067  .215  890  713  536  358  181 

.886  .215  004  827  650  472  295  .214  118  940  763  586  408 

.887  .213  231  054  876  699  521  .212  344  166  989  811  634 

.888  .211456  278  101  923  745  .210568  390  212  035  857 

.889  .209  679  501  323  146  968  .208  790  612  434  256  078 

.890  .207  900  722  544  366  188  .207  010  832  654  475  297 

.891  .206  119  941  763  584  406  .205  228  049  871  693  514 

.892  .204  336  158  979  801  622  .203  444  265  087  908  730 

.893  .202  551  372  194  015  836  .201658  479  300  122  943 

.894  .200  764  585  406  228  049  .199  870  691  512  333  154 

.895  .198  975  796  617  438  259  .198  080  901  722  542  363 

.896  .197184  005  826  646  467  .196288  108  929  750  570 

.897  .195  391  212  032  853  673  .194  494  314  135  955  776 

.898  .193  596  416  237  057  877  .192  698  518  338  159  979 

.899  .191799  619  439  260  080  .190  900  720  540  360  180 

.900  .190  000  820  640  460  280  .189100  920  740  559  379 

(47) 


Table  11.     Values  of  1— r^ 

r       0  12  3  4  S  6  7  8  9 

.900  .190  000  820  640  460  280  .189100  920  740  559  379 

.901  .188  199  019  839  658  478  .187  298  117  937  757  576 

.902  .186  396  216  035  855  674  .185  494  313  133  952  772 

.903  .184  591  410  230  049  868  .183  688  507  326  146  965 

.904  .182  784  603  422  242  061  .181880  699  518  337  156 

.905  .180  975  794  613  432  251  .180  070  889  708  526  345 

.906  .179164  983  802  620  439  .178258  076  895  714  532 

.907  .177  351  170  988  807  625  .176  444  262  081  899  718 

.908  .175  536  354  173  991  809  .174  628  446  264  083  901 

.909  .173  719  537  355  174  992  .172  810  628  446  264  082 

.910  .171900  718  536  354  172  .170  990  808  626  443  261 

.911  .170  079  897  715  532  350  .169  168  985  803  621  438 

.912  .168  256  074  891  709  526  .167  344  161  979  796  614 

.913  .166  431  248  066  883  700  .165  518  335  152  970  787 

.914  .164  604  421  238  056  873  .163  690  507  324  141  958 

.915  .162  775  592  409  226  043  .161860  677  494  310  127 

.916  .160  944  761  578  394  211  .160  028  844  661  478  294 

.917  .159  111  928  744  561  377  .158  194  010  827  643  460 

.918  .157  276  092  909  725  541  .156  358  174  990  807  623 

.919  .155439  255  071  888  704  .154  520  336  152  968  784 

.920  .153  600  416  232  048  864  .152  680  496  312  127  943 

.921  .151759  575  391  206  022  .150838  653  469  285  100 

.922  .149  916  732  547  363  178  .148  994  809  625  440  256 

.923  .148  071  886  702  517  332  .147  148  963  778  594  409 

.924  .146  224  039  854  670  485  .145  300  115  930  745  560 

.925  .144  375  190  005  820  635  .143  450  265  080  894  709 

.926  .142  524  339  154  968  783  .141598  412  227  042  856 

.927  .140  671  486  300  115  929  .139  744  558  373  187  002 

.928  .138  816  630  445  259  073  .137  888  702  516  331  145 

.929  .136  959  773  587  402  216  .136  030  844  658  472  286 

.930  .135  100  914  728  542  356  .134  170  984  798  611  425 

.931  .133  239  053  867  680  494  .132  308  121  935  749  562 

.932  .131376  190  003  817  630  .130444  257  071  884  698 

.933  .129  511  324  138  951  764  .128  578  391  204  018  831 

.934  .127  644  457  270  084  897  .126  710  523  336  149  962 

.935  .125  775  588  401  214  027  .124  840  653  466  278  091 

.936  .123  904  717  530  342  155  .122  968  780  593  406  218 

.937  .122  031  844  656  469  281  .121094  906  719  531  344 

.938  .120  156  968  781  593  405  .119  218  030  842  655  467 

.939  .118  279  091  903  716  528  .117  340  152  964  776  588 

.940  .116  400  212  024  836  648  .115  460  272  084  895  707 

.941  .114  519  331  143  954  766  .113  578  389  201  013  824 

.942  .112636  448  259  071  882  .111694  505  317  128  940 

.943  .110  751  562  374  185  996  .109  808  619  430  242  053 

.944  .108  864  675  486  298  109  .107  920  731  542  353  164 

.945  .106  975  786  597  408  219  .106  030  841  652  462  273 

.946  .105  084  895  706  516  327  .104  138  948  759  570  380 

.947  .103  191  002  812  623  433  .102  244  054  865  675  486 

.948  .101296  106  917  727  537  .100348  158  9683  7786  5888 

.949  .099  3990  2092  0194  8295  6396  .098  4497  2598  0699  8800  6900 

.950  .097  5000  3100  1200  9299  7398  .096  5497  3596  1695  9794  7892 

(48) 


Table  II.     Values  of  1 — r^ 


r 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

950 

.097  5000 

3100 

1200 

9299 

7398 

.096  5497 

3596 

1695 

9794 

7892 

951 

.095  5990 

4088 

2186 

0283 

8380 

.094  6477 

4574 

2671 

0768 

8864 

952 

.093  6960 

5056 

3152 

1247 

9342 

.092  7437 

5532 

3627 

1722 

9816 

953 

.091  7910 

6004 

4098 

2191 

0284 

.090  8377 

6470 

4563 

2656 

0748 

954 

.089  8840 

6932 

5024 

3115 

1206 

.088  9297 

7388 

5479 

3570 

1660 

955 

.087  9750 

7840 

5930 

4019 

2108 

.087  0197 

8286 

6375 

4464 

2552 

.956 

.086  0640 

8728 

6816 

4903 

2990 

.085  1077 

9164 

7251 

5338 

3424 

957 

.084  1510 

9596 

7682 

5767 

3852 

.083  1937 

0022 

8107 

6192 

4276 

958 

.  082  2360 

0444 

8528 

6611 

4694 

.081  2777 

0860 

8943 

'7026 

5108 

959 

.080  3190 

1272 

9354 

7435 

5516 

.079  3597 

1678 

9759 

7840 

5920 

960 

.  078  4000 

2080 

0160 

8239 

6318 

.  077  4397 

2476 

0555 

8634 

6712 

.961 

.076  4790 

2868 

0946 

9023 

7100 

.075  5177 

3254 

1331 

9408 

7484 

962 

.074  5560 

3636 

1712 

9787 

7862 

.  073  5937 

4012 

2087 

0162 

8236 

963 

.072  6310 

4384 

2458 

0531 

8604 

.071  6677 

4750 

2823 

0896 

8968 

964 

.070  7040 

5112 

3184 

1255 

9326 

.069  7397 

5468 

3539 

1610 

9680 

965 

.068  7750 

5820 

3890 

1959 

0028 

.067  8097 

6166 

4235 

2304 

0372 

.966 

.  066  8440 

6508 

4576 

2643 

0710 

.065  8777 

6844 

4911 

2978 

1044 

.967 

.064  9110 

7176 

5242 

3307 

1372 

.  063  9437 

7502 

5567 

3632 

1696 

.968 

.062  9760 

7824 

5888 

3951 

2014 

.062  0077 

8140 

6203 

4266 

2328 

.969 

.061  0390 

8452 

6514 

4575 

2636 

.060  0697 

8758 

6819 

4880 

2940 

.970 

.059  1000 

9060 

7120 

5179 

3238 

.058  1297 

9356 

74V15 

5474 

3532 

.971 

.057  1590 

9648 

7706 

5763 

3820 

.056  1877 

9934 

7991 

6048 

4104 

.972 

.055  2160 

0216 

8272 

6327 

4382 

.  054  2437 

0492 

8547 

6602 

4656 

.973 

.053  2710 

0764 

8818 

6871 

4924 

.052  2977 

1030 

9083 

7136 

5188 

.974 

.051  3240 

1292 

9344 

7395 

5446 

.050  3497 

1548 

9599 

7650 

5700 

.975 

.049  3750 

1800 

9850 

7899 

5948 

.048  3997 

2046 

0095 

8144 

6192 

.976 

.047  4240 

2288 

0336 

8383 

6430 

.  046  4477 

2524 

0571 

8618 

6664 

.977 

.045  4710 

2756 

0802 

8847 

6892 

.044  4937 

2982 

1027 

9072 

7116 

.978 

.043  5160 

3204 

1248 

9291 

7334 

.042  5377 

3420 

1463 

9506 

7548 

.979 

.041  5590 

3632 

1674 

9715 

7756 

.040  5797 

3838 

1879 

9920 

7960 

.980 

.039  6000 

4040 

2080 

0119 

8158 

.038  6197 

4236 

2275 

0314 

8352 

.981 

.037  6390 

4428 

2466 

0503 

8540 

.036  6577 

4614 

2651 

0688 

8724 

.982 

.035  6760 

4796 

2832 

0867 

8902 

.  034  6937 

4972 

3007 

1042 

9076 

.983 

.033  7110 

5144 

3178 

1211 

9244 

.032  7277 

5310 

3343 

1376 

9408 

.984 

.031  7440 

5472 

3504 

1535 

9566 

.030  7597 

5628 

3659 

1690 

9720 

.985 

.  029  7750 

5780 

3810 

1839 

9868 

.028  7897 

5926 

3955 

1984 

0012 

.986 

.027  8040 

6068 

4096 

2123 

0150 

.026  8177 

6204 

4231 

2258 

0284 

.987 

.025  8310 

6336 

4362 

2387 

0412 

.  024  8437 

6462 

4487 

2512 

0536 

.988 

.023  8560 

6584 

4608 

2631 

0654 

.022  8677 

6700 

4723 

2746 

0768 

.989 

.021  8790 

6812 

4834 

2855 

0876 

.020  8897 

6918 

4939 

2960 

0980 

.990 

.019  9000 

7020 

5040 

3059 

1078 

.018  9097 

7116 

5135 

3154 

1172 

.991 

.017  9190 

7208 

5226 

3243 

1260 

.016  9277 

7294 

5311 

3328 

1344 

.992 

.015  9360 

7376 

5392 

3407 

1422 

.014  9437 

7452 

5467 

3482 

1496 

.993 

.013  9510 

7524 

5538 

3551 

1564 

.012  9577 

7590 

5603 

3616 

1628 

.994 

.011  9640 

7652 

5664 

3675 

1686 

.010  9697 

7708 

5719 

3730 

1740 

.995 

.009  97500 

77599 

57696 

37791 

17884 

.008  97975 

78064 

58151 

38236 

18319 

.996 

.007  98400 

78479 

58556 

38631 

18704 

.006  98775 

78844 

58911 

38976 

19039 

.997 

.005  99100 

79159 

59216 

39271 

19324 

.004  99375 

79424 

59471 

39516 

19559 

.998 

.003  99600 

79639 

59676 

39711 

19744 

.002  99775 

79804 

59831 

39856 

19879 

.999 

.001  99900 

79919 

59936 

39951 

19964 

.000  99975 

79984 

59991 

39996 

19999 

(49) 


m 


I 
I 


SCIENCE  AND  ENGINEERING 

LIBRARY 

University  of  California, 

San  Diego 


DAT 

F.    DIIF. 

SE   16 

VCSD  Libr. 

UC  SOUTHERN  REGIONAL  LIBRARY  FACILITY 


A  A  001  421  957 


F'f  B  2  z  1980 


ill 


